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Simplifying 10x2 + -2x + -20 = 0 Reorder the terms: -20 + -2x + 10x2 = 0 Solving -20 + -2x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -1x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + -1x + 5x2)' equal to zero and attempt to solve: Simplifying -10 + -1x + 5x2 = 0 Solving -10 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2 + -0.2x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -0.2x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -0.2x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -0.2x + x2 = 0 + 2 -0.2x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -0.2x + x2 = 2 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 2 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 2 + 0.01 Combine like terms: 2 + 0.01 = 2.01 0.01 + -0.2x + x2 = 2.01 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 2.01 Calculate the square root of the right side: 1.417744688 Break this problem into two subproblems by setting (x + -0.1) equal to 1.417744688 and -1.417744688.Subproblem 1
x + -0.1 = 1.417744688 Simplifying x + -0.1 = 1.417744688 Reorder the terms: -0.1 + x = 1.417744688 Solving -0.1 + x = 1.417744688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 1.417744688 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 1.417744688 + 0.1 x = 1.417744688 + 0.1 Combine like terms: 1.417744688 + 0.1 = 1.517744688 x = 1.517744688 Simplifying x = 1.517744688Subproblem 2
x + -0.1 = -1.417744688 Simplifying x + -0.1 = -1.417744688 Reorder the terms: -0.1 + x = -1.417744688 Solving -0.1 + x = -1.417744688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -1.417744688 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -1.417744688 + 0.1 x = -1.417744688 + 0.1 Combine like terms: -1.417744688 + 0.1 = -1.317744688 x = -1.317744688 Simplifying x = -1.317744688Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.517744688, -1.317744688}Solution
x = {1.517744688, -1.317744688}
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