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Simplifying -80x2 + 120x + 610 = 130 Reorder the terms: 610 + 120x + -80x2 = 130 Solving 610 + 120x + -80x2 = 130 Solving for variable 'x'. Reorder the terms: 610 + -130 + 120x + -80x2 = 130 + -130 Combine like terms: 610 + -130 = 480 480 + 120x + -80x2 = 130 + -130 Combine like terms: 130 + -130 = 0 480 + 120x + -80x2 = 0 Factor out the Greatest Common Factor (GCF), '40'. 40(12 + 3x + -2x2) = 0 Ignore the factor 40.Subproblem 1
Set the factor '(12 + 3x + -2x2)' equal to zero and attempt to solve: Simplifying 12 + 3x + -2x2 = 0 Solving 12 + 3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -6 + -1.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -1.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + -1.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1.5x + x2 = 0 + 6 -1.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 -1.5x + x2 = 6 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 6 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 6 + 0.5625 Combine like terms: 6 + 0.5625 = 6.5625 0.5625 + -1.5x + x2 = 6.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (x + -0.75) equal to 2.561737691 and -2.561737691.Subproblem 1
x + -0.75 = 2.561737691 Simplifying x + -0.75 = 2.561737691 Reorder the terms: -0.75 + x = 2.561737691 Solving -0.75 + x = 2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 2.561737691 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.561737691 + 0.75 x = 2.561737691 + 0.75 Combine like terms: 2.561737691 + 0.75 = 3.311737691 x = 3.311737691 Simplifying x = 3.311737691Subproblem 2
x + -0.75 = -2.561737691 Simplifying x + -0.75 = -2.561737691 Reorder the terms: -0.75 + x = -2.561737691 Solving -0.75 + x = -2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -2.561737691 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.561737691 + 0.75 x = -2.561737691 + 0.75 Combine like terms: -2.561737691 + 0.75 = -1.811737691 x = -1.811737691 Simplifying x = -1.811737691Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.311737691, -1.811737691}Solution
x = {3.311737691, -1.811737691}
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