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Simplifying 10x2 + -2x + -160 = 0 Reorder the terms: -160 + -2x + 10x2 = 0 Solving -160 + -2x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-80 + -1x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-80 + -1x + 5x2)' equal to zero and attempt to solve: Simplifying -80 + -1x + 5x2 = 0 Solving -80 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -16 + -0.2x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -0.2x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -0.2x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -0.2x + x2 = 0 + 16 -0.2x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -0.2x + x2 = 16 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 = 16 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 16 + 0.01 Combine like terms: 16 + 0.01 = 16.01 0.01 + -0.2x + x2 = 16.01 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 16.01 Calculate the square root of the right side: 4.001249805 Break this problem into two subproblems by setting (x + -0.1) equal to 4.001249805 and -4.001249805.Subproblem 1
x + -0.1 = 4.001249805 Simplifying x + -0.1 = 4.001249805 Reorder the terms: -0.1 + x = 4.001249805 Solving -0.1 + x = 4.001249805 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 = 4.001249805 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 4.001249805 + 0.1 x = 4.001249805 + 0.1 Combine like terms: 4.001249805 + 0.1 = 4.101249805 x = 4.101249805 Simplifying x = 4.101249805Subproblem 2
x + -0.1 = -4.001249805 Simplifying x + -0.1 = -4.001249805 Reorder the terms: -0.1 + x = -4.001249805 Solving -0.1 + x = -4.001249805 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 = -4.001249805 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -4.001249805 + 0.1 x = -4.001249805 + 0.1 Combine like terms: -4.001249805 + 0.1 = -3.901249805 x = -3.901249805 Simplifying x = -3.901249805Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.101249805, -3.901249805}Solution
x = {4.101249805, -3.901249805}
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