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Simplifying 5x2 + -15x + -10 = 20 Reorder the terms: -10 + -15x + 5x2 = 20 Solving -10 + -15x + 5x2 = 20 Solving for variable 'x'. Reorder the terms: -10 + -20 + -15x + 5x2 = 20 + -20 Combine like terms: -10 + -20 = -30 -30 + -15x + 5x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -30 + -15x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-6 + -3x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-6 + -3x + x2)' equal to zero and attempt to solve: Simplifying -6 + -3x + x2 = 0 Solving -6 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -3x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -3x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -3x + x2 = 0 + 6 -3x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -3x + x2 = 6 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 6 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 6 + 2.25 Combine like terms: 6 + 2.25 = 8.25 2.25 + -3x + x2 = 8.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + -1.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x + -1.5 = 2.872281323 Simplifying x + -1.5 = 2.872281323 Reorder the terms: -1.5 + x = 2.872281323 Solving -1.5 + x = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 2.872281323 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 2.872281323 + 1.5 x = 2.872281323 + 1.5 Combine like terms: 2.872281323 + 1.5 = 4.372281323 x = 4.372281323 Simplifying x = 4.372281323Subproblem 2
x + -1.5 = -2.872281323 Simplifying x + -1.5 = -2.872281323 Reorder the terms: -1.5 + x = -2.872281323 Solving -1.5 + x = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -2.872281323 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -2.872281323 + 1.5 x = -2.872281323 + 1.5 Combine like terms: -2.872281323 + 1.5 = -1.372281323 x = -1.372281323 Simplifying x = -1.372281323Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.372281323, -1.372281323}Solution
x = {4.372281323, -1.372281323}
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