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Simplifying (10x + -15)(10x + -15) + -80 = 0 Reorder the terms: (-15 + 10x)(10x + -15) + -80 = 0 Reorder the terms: (-15 + 10x)(-15 + 10x) + -80 = 0 Multiply (-15 + 10x) * (-15 + 10x) (-15(-15 + 10x) + 10x * (-15 + 10x)) + -80 = 0 ((-15 * -15 + 10x * -15) + 10x * (-15 + 10x)) + -80 = 0 ((225 + -150x) + 10x * (-15 + 10x)) + -80 = 0 (225 + -150x + (-15 * 10x + 10x * 10x)) + -80 = 0 (225 + -150x + (-150x + 100x2)) + -80 = 0 Combine like terms: -150x + -150x = -300x (225 + -300x + 100x2) + -80 = 0 Reorder the terms: 225 + -80 + -300x + 100x2 = 0 Combine like terms: 225 + -80 = 145 145 + -300x + 100x2 = 0 Solving 145 + -300x + 100x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(29 + -60x + 20x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(29 + -60x + 20x2)' equal to zero and attempt to solve: Simplifying 29 + -60x + 20x2 = 0 Solving 29 + -60x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 1.45 + -3x + x2 = 0.0 Move the constant term to the right: Add '-1.45' to each side of the equation. 1.45 + -3x + -1.45 + x2 = 0.0 + -1.45 Reorder the terms: 1.45 + -1.45 + -3x + x2 = 0.0 + -1.45 Combine like terms: 1.45 + -1.45 = 0.00 0.00 + -3x + x2 = 0.0 + -1.45 -3x + x2 = 0.0 + -1.45 Combine like terms: 0.0 + -1.45 = -1.45 -3x + x2 = -1.45 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -1.45 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.45 + 2.25 Combine like terms: -1.45 + 2.25 = 0.8 2.25 + -3x + x2 = 0.8 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.8 Calculate the square root of the right side: 0.894427191 Break this problem into two subproblems by setting (x + -1.5) equal to 0.894427191 and -0.894427191.Subproblem 1
x + -1.5 = 0.894427191 Simplifying x + -1.5 = 0.894427191 Reorder the terms: -1.5 + x = 0.894427191 Solving -1.5 + x = 0.894427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.894427191 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.894427191 + 1.5 x = 0.894427191 + 1.5 Combine like terms: 0.894427191 + 1.5 = 2.394427191 x = 2.394427191 Simplifying x = 2.394427191Subproblem 2
x + -1.5 = -0.894427191 Simplifying x + -1.5 = -0.894427191 Reorder the terms: -1.5 + x = -0.894427191 Solving -1.5 + x = -0.894427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.894427191 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.894427191 + 1.5 x = -0.894427191 + 1.5 Combine like terms: -0.894427191 + 1.5 = 0.605572809 x = 0.605572809 Simplifying x = 0.605572809Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.394427191, 0.605572809}Solution
x = {2.394427191, 0.605572809}
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