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Simplifying 10x2 + -18x + -60 = 0 Reorder the terms: -60 + -18x + 10x2 = 0 Solving -60 + -18x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-30 + -9x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-30 + -9x + 5x2)' equal to zero and attempt to solve: Simplifying -30 + -9x + 5x2 = 0 Solving -30 + -9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6 + -1.8x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -1.8x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -1.8x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1.8x + x2 = 0 + 6 -1.8x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1.8x + x2 = 6 The x term is -1.8x. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x + 0.81 + x2 = 6 + 0.81 Reorder the terms: 0.81 + -1.8x + x2 = 6 + 0.81 Combine like terms: 6 + 0.81 = 6.81 0.81 + -1.8x + x2 = 6.81 Factor a perfect square on the left side: (x + -0.9)(x + -0.9) = 6.81 Calculate the square root of the right side: 2.60959767 Break this problem into two subproblems by setting (x + -0.9) equal to 2.60959767 and -2.60959767.Subproblem 1
x + -0.9 = 2.60959767 Simplifying x + -0.9 = 2.60959767 Reorder the terms: -0.9 + x = 2.60959767 Solving -0.9 + x = 2.60959767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = 2.60959767 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = 2.60959767 + 0.9 x = 2.60959767 + 0.9 Combine like terms: 2.60959767 + 0.9 = 3.50959767 x = 3.50959767 Simplifying x = 3.50959767Subproblem 2
x + -0.9 = -2.60959767 Simplifying x + -0.9 = -2.60959767 Reorder the terms: -0.9 + x = -2.60959767 Solving -0.9 + x = -2.60959767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9' to each side of the equation. -0.9 + 0.9 + x = -2.60959767 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + x = -2.60959767 + 0.9 x = -2.60959767 + 0.9 Combine like terms: -2.60959767 + 0.9 = -1.70959767 x = -1.70959767 Simplifying x = -1.70959767Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.50959767, -1.70959767}Solution
x = {3.50959767, -1.70959767}
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