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Simplifying 7 + 3x + (6x + -4) * 3x = 80 Reorder the terms: 7 + 3x + (-4 + 6x) * 3x = 80 Reorder the terms for easier multiplication: 7 + 3x + 3x(-4 + 6x) = 80 7 + 3x + (-4 * 3x + 6x * 3x) = 80 7 + 3x + (-12x + 18x2) = 80 Combine like terms: 3x + -12x = -9x 7 + -9x + 18x2 = 80 Solving 7 + -9x + 18x2 = 80 Solving for variable 'x'. Reorder the terms: 7 + -80 + -9x + 18x2 = 80 + -80 Combine like terms: 7 + -80 = -73 -73 + -9x + 18x2 = 80 + -80 Combine like terms: 80 + -80 = 0 -73 + -9x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -4.055555556 + -0.5x + x2 = 0 Move the constant term to the right: Add '4.055555556' to each side of the equation. -4.055555556 + -0.5x + 4.055555556 + x2 = 0 + 4.055555556 Reorder the terms: -4.055555556 + 4.055555556 + -0.5x + x2 = 0 + 4.055555556 Combine like terms: -4.055555556 + 4.055555556 = 0.000000000 0.000000000 + -0.5x + x2 = 0 + 4.055555556 -0.5x + x2 = 0 + 4.055555556 Combine like terms: 0 + 4.055555556 = 4.055555556 -0.5x + x2 = 4.055555556 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 4.055555556 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 4.055555556 + 0.0625 Combine like terms: 4.055555556 + 0.0625 = 4.118055556 0.0625 + -0.5x + x2 = 4.118055556 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 4.118055556 Calculate the square root of the right side: 2.029299277 Break this problem into two subproblems by setting (x + -0.25) equal to 2.029299277 and -2.029299277.Subproblem 1
x + -0.25 = 2.029299277 Simplifying x + -0.25 = 2.029299277 Reorder the terms: -0.25 + x = 2.029299277 Solving -0.25 + x = 2.029299277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.029299277 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.029299277 + 0.25 x = 2.029299277 + 0.25 Combine like terms: 2.029299277 + 0.25 = 2.279299277 x = 2.279299277 Simplifying x = 2.279299277Subproblem 2
x + -0.25 = -2.029299277 Simplifying x + -0.25 = -2.029299277 Reorder the terms: -0.25 + x = -2.029299277 Solving -0.25 + x = -2.029299277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.029299277 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.029299277 + 0.25 x = -2.029299277 + 0.25 Combine like terms: -2.029299277 + 0.25 = -1.779299277 x = -1.779299277 Simplifying x = -1.779299277Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.279299277, -1.779299277}
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