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Simplifying 2x(5x + -1) = 90 Reorder the terms: 2x(-1 + 5x) = 90 (-1 * 2x + 5x * 2x) = 90 (-2x + 10x2) = 90 Solving -2x + 10x2 = 90 Solving for variable 'x'. Reorder the terms: -90 + -2x + 10x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -2x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + -1x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + -1x + 5x2)' equal to zero and attempt to solve: Simplifying -45 + -1x + 5x2 = 0 Solving -45 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -9 + -0.2x + x2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -0.2x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -0.2x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -0.2x + x2 = 0 + 9 -0.2x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -0.2x + x2 = 9 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 = 9 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 9 + 0.01 Combine like terms: 9 + 0.01 = 9.01 0.01 + -0.2x + x2 = 9.01 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 9.01 Calculate the square root of the right side: 3.001666204 Break this problem into two subproblems by setting (x + -0.1) equal to 3.001666204 and -3.001666204.Subproblem 1
x + -0.1 = 3.001666204 Simplifying x + -0.1 = 3.001666204 Reorder the terms: -0.1 + x = 3.001666204 Solving -0.1 + x = 3.001666204 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 = 3.001666204 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 3.001666204 + 0.1 x = 3.001666204 + 0.1 Combine like terms: 3.001666204 + 0.1 = 3.101666204 x = 3.101666204 Simplifying x = 3.101666204Subproblem 2
x + -0.1 = -3.001666204 Simplifying x + -0.1 = -3.001666204 Reorder the terms: -0.1 + x = -3.001666204 Solving -0.1 + x = -3.001666204 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 = -3.001666204 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -3.001666204 + 0.1 x = -3.001666204 + 0.1 Combine like terms: -3.001666204 + 0.1 = -2.901666204 x = -2.901666204 Simplifying x = -2.901666204Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.101666204, -2.901666204}Solution
x = {3.101666204, -2.901666204}
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