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Simplifying 7x(5x + -19) = 35 Reorder the terms: 7x(-19 + 5x) = 35 (-19 * 7x + 5x * 7x) = 35 (-133x + 35x2) = 35 Solving -133x + 35x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + -133x + 35x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -133x + 35x2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-5 + -19x + 5x2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-5 + -19x + 5x2)' equal to zero and attempt to solve: Simplifying -5 + -19x + 5x2 = 0 Solving -5 + -19x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -3.8x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -3.8x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -3.8x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3.8x + x2 = 0 + 1 -3.8x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3.8x + x2 = 1 The x term is -3.8x. Take half its coefficient (-1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. -3.8x + 3.61 + x2 = 1 + 3.61 Reorder the terms: 3.61 + -3.8x + x2 = 1 + 3.61 Combine like terms: 1 + 3.61 = 4.61 3.61 + -3.8x + x2 = 4.61 Factor a perfect square on the left side: (x + -1.9)(x + -1.9) = 4.61 Calculate the square root of the right side: 2.147091055 Break this problem into two subproblems by setting (x + -1.9) equal to 2.147091055 and -2.147091055.Subproblem 1
x + -1.9 = 2.147091055 Simplifying x + -1.9 = 2.147091055 Reorder the terms: -1.9 + x = 2.147091055 Solving -1.9 + x = 2.147091055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = 2.147091055 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = 2.147091055 + 1.9 x = 2.147091055 + 1.9 Combine like terms: 2.147091055 + 1.9 = 4.047091055 x = 4.047091055 Simplifying x = 4.047091055Subproblem 2
x + -1.9 = -2.147091055 Simplifying x + -1.9 = -2.147091055 Reorder the terms: -1.9 + x = -2.147091055 Solving -1.9 + x = -2.147091055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = -2.147091055 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = -2.147091055 + 1.9 x = -2.147091055 + 1.9 Combine like terms: -2.147091055 + 1.9 = -0.247091055 x = -0.247091055 Simplifying x = -0.247091055Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.047091055, -0.247091055}Solution
x = {4.047091055, -0.247091055}
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