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Simplifying 12x2 + 15x = 180 Reorder the terms: 15x + 12x2 = 180 Solving 15x + 12x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 15x + 12x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 15x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-60 + 5x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-60 + 5x + 4x2)' equal to zero and attempt to solve: Simplifying -60 + 5x + 4x2 = 0 Solving -60 + 5x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -15 + 1.25x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 1.25x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 1.25x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 1.25x + x2 = 0 + 15 1.25x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 1.25x + x2 = 15 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 15 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 15 + 0.390625 Combine like terms: 15 + 0.390625 = 15.390625 0.390625 + 1.25x + x2 = 15.390625 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 15.390625 Calculate the square root of the right side: 3.923088707 Break this problem into two subproblems by setting (x + 0.625) equal to 3.923088707 and -3.923088707.Subproblem 1
x + 0.625 = 3.923088707 Simplifying x + 0.625 = 3.923088707 Reorder the terms: 0.625 + x = 3.923088707 Solving 0.625 + x = 3.923088707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 3.923088707 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 3.923088707 + -0.625 x = 3.923088707 + -0.625 Combine like terms: 3.923088707 + -0.625 = 3.298088707 x = 3.298088707 Simplifying x = 3.298088707Subproblem 2
x + 0.625 = -3.923088707 Simplifying x + 0.625 = -3.923088707 Reorder the terms: 0.625 + x = -3.923088707 Solving 0.625 + x = -3.923088707 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -3.923088707 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -3.923088707 + -0.625 x = -3.923088707 + -0.625 Combine like terms: -3.923088707 + -0.625 = -4.548088707 x = -4.548088707 Simplifying x = -4.548088707Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.298088707, -4.548088707}Solution
x = {3.298088707, -4.548088707}
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