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Simplifying 4(x2 + 19x + -140) = 0 Reorder the terms: 4(-140 + 19x + x2) = 0 (-140 * 4 + 19x * 4 + x2 * 4) = 0 (-560 + 76x + 4x2) = 0 Solving -560 + 76x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-140 + 19x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-140 + 19x + x2)' equal to zero and attempt to solve: Simplifying -140 + 19x + x2 = 0 Solving -140 + 19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + 19x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + 19x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + 19x + x2 = 0 + 140 19x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 19x + x2 = 140 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = 140 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 140 + 90.25 Combine like terms: 140 + 90.25 = 230.25 90.25 + 19x + x2 = 230.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 230.25 Calculate the square root of the right side: 15.173990905 Break this problem into two subproblems by setting (x + 9.5) equal to 15.173990905 and -15.173990905.Subproblem 1
x + 9.5 = 15.173990905 Simplifying x + 9.5 = 15.173990905 Reorder the terms: 9.5 + x = 15.173990905 Solving 9.5 + x = 15.173990905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 15.173990905 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 15.173990905 + -9.5 x = 15.173990905 + -9.5 Combine like terms: 15.173990905 + -9.5 = 5.673990905 x = 5.673990905 Simplifying x = 5.673990905Subproblem 2
x + 9.5 = -15.173990905 Simplifying x + 9.5 = -15.173990905 Reorder the terms: 9.5 + x = -15.173990905 Solving 9.5 + x = -15.173990905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -15.173990905 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -15.173990905 + -9.5 x = -15.173990905 + -9.5 Combine like terms: -15.173990905 + -9.5 = -24.673990905 x = -24.673990905 Simplifying x = -24.673990905Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.673990905, -24.673990905}Solution
x = {5.673990905, -24.673990905}
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