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Simplifying 99x(6x + 10) + 5 = 4x(2x + 6) + -3 Reorder the terms: 99x(10 + 6x) + 5 = 4x(2x + 6) + -3 (10 * 99x + 6x * 99x) + 5 = 4x(2x + 6) + -3 (990x + 594x2) + 5 = 4x(2x + 6) + -3 Reorder the terms: 5 + 990x + 594x2 = 4x(2x + 6) + -3 Reorder the terms: 5 + 990x + 594x2 = 4x(6 + 2x) + -3 5 + 990x + 594x2 = (6 * 4x + 2x * 4x) + -3 5 + 990x + 594x2 = (24x + 8x2) + -3 Reorder the terms: 5 + 990x + 594x2 = -3 + 24x + 8x2 Solving 5 + 990x + 594x2 = -3 + 24x + 8x2 Solving for variable 'x'. Reorder the terms: 5 + 3 + 990x + -24x + 594x2 + -8x2 = -3 + 24x + 8x2 + 3 + -24x + -8x2 Combine like terms: 5 + 3 = 8 8 + 990x + -24x + 594x2 + -8x2 = -3 + 24x + 8x2 + 3 + -24x + -8x2 Combine like terms: 990x + -24x = 966x 8 + 966x + 594x2 + -8x2 = -3 + 24x + 8x2 + 3 + -24x + -8x2 Combine like terms: 594x2 + -8x2 = 586x2 8 + 966x + 586x2 = -3 + 24x + 8x2 + 3 + -24x + -8x2 Reorder the terms: 8 + 966x + 586x2 = -3 + 3 + 24x + -24x + 8x2 + -8x2 Combine like terms: -3 + 3 = 0 8 + 966x + 586x2 = 0 + 24x + -24x + 8x2 + -8x2 8 + 966x + 586x2 = 24x + -24x + 8x2 + -8x2 Combine like terms: 24x + -24x = 0 8 + 966x + 586x2 = 0 + 8x2 + -8x2 8 + 966x + 586x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 8 + 966x + 586x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 483x + 293x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 483x + 293x2)' equal to zero and attempt to solve: Simplifying 4 + 483x + 293x2 = 0 Solving 4 + 483x + 293x2 = 0 Begin completing the square. Divide all terms by 293 the coefficient of the squared term: Divide each side by '293'. 0.01365187713 + 1.648464164x + x2 = 0 Move the constant term to the right: Add '-0.01365187713' to each side of the equation. 0.01365187713 + 1.648464164x + -0.01365187713 + x2 = 0 + -0.01365187713 Reorder the terms: 0.01365187713 + -0.01365187713 + 1.648464164x + x2 = 0 + -0.01365187713 Combine like terms: 0.01365187713 + -0.01365187713 = 0.00000000000 0.00000000000 + 1.648464164x + x2 = 0 + -0.01365187713 1.648464164x + x2 = 0 + -0.01365187713 Combine like terms: 0 + -0.01365187713 = -0.01365187713 1.648464164x + x2 = -0.01365187713 The x term is 1.648464164x. Take half its coefficient (0.824232082). Square it (0.6793585250) and add it to both sides. Add '0.6793585250' to each side of the equation. 1.648464164x + 0.6793585250 + x2 = -0.01365187713 + 0.6793585250 Reorder the terms: 0.6793585250 + 1.648464164x + x2 = -0.01365187713 + 0.6793585250 Combine like terms: -0.01365187713 + 0.6793585250 = 0.66570664787 0.6793585250 + 1.648464164x + x2 = 0.66570664787 Factor a perfect square on the left side: (x + 0.824232082)(x + 0.824232082) = 0.66570664787 Calculate the square root of the right side: 0.81590848 Break this problem into two subproblems by setting (x + 0.824232082) equal to 0.81590848 and -0.81590848.Subproblem 1
x + 0.824232082 = 0.81590848 Simplifying x + 0.824232082 = 0.81590848 Reorder the terms: 0.824232082 + x = 0.81590848 Solving 0.824232082 + x = 0.81590848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.824232082' to each side of the equation. 0.824232082 + -0.824232082 + x = 0.81590848 + -0.824232082 Combine like terms: 0.824232082 + -0.824232082 = 0.000000000 0.000000000 + x = 0.81590848 + -0.824232082 x = 0.81590848 + -0.824232082 Combine like terms: 0.81590848 + -0.824232082 = -0.008323602 x = -0.008323602 Simplifying x = -0.008323602Subproblem 2
x + 0.824232082 = -0.81590848 Simplifying x + 0.824232082 = -0.81590848 Reorder the terms: 0.824232082 + x = -0.81590848 Solving 0.824232082 + x = -0.81590848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.824232082' to each side of the equation. 0.824232082 + -0.824232082 + x = -0.81590848 + -0.824232082 Combine like terms: 0.824232082 + -0.824232082 = 0.000000000 0.000000000 + x = -0.81590848 + -0.824232082 x = -0.81590848 + -0.824232082 Combine like terms: -0.81590848 + -0.824232082 = -1.640140562 x = -1.640140562 Simplifying x = -1.640140562Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.008323602, -1.640140562}Solution
x = {-0.008323602, -1.640140562}
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