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Simplifying 3x2 + -60x + 108 + x2 = x(x + 74) + -50x Reorder the terms: 108 + -60x + 3x2 + x2 = x(x + 74) + -50x Combine like terms: 3x2 + x2 = 4x2 108 + -60x + 4x2 = x(x + 74) + -50x Reorder the terms: 108 + -60x + 4x2 = x(74 + x) + -50x 108 + -60x + 4x2 = (74 * x + x * x) + -50x 108 + -60x + 4x2 = (74x + x2) + -50x Reorder the terms: 108 + -60x + 4x2 = 74x + -50x + x2 Combine like terms: 74x + -50x = 24x 108 + -60x + 4x2 = 24x + x2 Solving 108 + -60x + 4x2 = 24x + x2 Solving for variable 'x'. Reorder the terms: 108 + -60x + -24x + 4x2 + -1x2 = 24x + x2 + -24x + -1x2 Combine like terms: -60x + -24x = -84x 108 + -84x + 4x2 + -1x2 = 24x + x2 + -24x + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 108 + -84x + 3x2 = 24x + x2 + -24x + -1x2 Reorder the terms: 108 + -84x + 3x2 = 24x + -24x + x2 + -1x2 Combine like terms: 24x + -24x = 0 108 + -84x + 3x2 = 0 + x2 + -1x2 108 + -84x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 108 + -84x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(36 + -28x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(36 + -28x + x2)' equal to zero and attempt to solve: Simplifying 36 + -28x + x2 = 0 Solving 36 + -28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -28x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -28x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -28x + x2 = 0 + -36 -28x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -28x + x2 = -36 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -36 + 196 Reorder the terms: 196 + -28x + x2 = -36 + 196 Combine like terms: -36 + 196 = 160 196 + -28x + x2 = 160 Factor a perfect square on the left side: (x + -14)(x + -14) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (x + -14) equal to 12.649110641 and -12.649110641.Subproblem 1
x + -14 = 12.649110641 Simplifying x + -14 = 12.649110641 Reorder the terms: -14 + x = 12.649110641 Solving -14 + x = 12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 12.649110641 + 14 Combine like terms: -14 + 14 = 0 0 + x = 12.649110641 + 14 x = 12.649110641 + 14 Combine like terms: 12.649110641 + 14 = 26.649110641 x = 26.649110641 Simplifying x = 26.649110641Subproblem 2
x + -14 = -12.649110641 Simplifying x + -14 = -12.649110641 Reorder the terms: -14 + x = -12.649110641 Solving -14 + x = -12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -12.649110641 + 14 Combine like terms: -14 + 14 = 0 0 + x = -12.649110641 + 14 x = -12.649110641 + 14 Combine like terms: -12.649110641 + 14 = 1.350889359 x = 1.350889359 Simplifying x = 1.350889359Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.649110641, 1.350889359}Solution
x = {26.649110641, 1.350889359}
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