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Simplifying -20x2 + -104x + 150 = 0 Reorder the terms: 150 + -104x + -20x2 = 0 Solving 150 + -104x + -20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(75 + -52x + -10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(75 + -52x + -10x2)' equal to zero and attempt to solve: Simplifying 75 + -52x + -10x2 = 0 Solving 75 + -52x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -7.5 + 5.2x + x2 = 0.0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 5.2x + 7.5 + x2 = 0.0 + 7.5 Reorder the terms: -7.5 + 7.5 + 5.2x + x2 = 0.0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 5.2x + x2 = 0.0 + 7.5 5.2x + x2 = 0.0 + 7.5 Combine like terms: 0.0 + 7.5 = 7.5 5.2x + x2 = 7.5 The x term is 5.2x. Take half its coefficient (2.6). Square it (6.76) and add it to both sides. Add '6.76' to each side of the equation. 5.2x + 6.76 + x2 = 7.5 + 6.76 Reorder the terms: 6.76 + 5.2x + x2 = 7.5 + 6.76 Combine like terms: 7.5 + 6.76 = 14.26 6.76 + 5.2x + x2 = 14.26 Factor a perfect square on the left side: (x + 2.6)(x + 2.6) = 14.26 Calculate the square root of the right side: 3.776241518 Break this problem into two subproblems by setting (x + 2.6) equal to 3.776241518 and -3.776241518.Subproblem 1
x + 2.6 = 3.776241518 Simplifying x + 2.6 = 3.776241518 Reorder the terms: 2.6 + x = 3.776241518 Solving 2.6 + x = 3.776241518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = 3.776241518 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = 3.776241518 + -2.6 x = 3.776241518 + -2.6 Combine like terms: 3.776241518 + -2.6 = 1.176241518 x = 1.176241518 Simplifying x = 1.176241518Subproblem 2
x + 2.6 = -3.776241518 Simplifying x + 2.6 = -3.776241518 Reorder the terms: 2.6 + x = -3.776241518 Solving 2.6 + x = -3.776241518 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.6' to each side of the equation. 2.6 + -2.6 + x = -3.776241518 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + x = -3.776241518 + -2.6 x = -3.776241518 + -2.6 Combine like terms: -3.776241518 + -2.6 = -6.376241518 x = -6.376241518 Simplifying x = -6.376241518Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.176241518, -6.376241518}Solution
x = {1.176241518, -6.376241518}
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