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Simplifying 12(x2 + -15x + 40) = 0 Reorder the terms: 12(40 + -15x + x2) = 0 (40 * 12 + -15x * 12 + x2 * 12) = 0 (480 + -180x + 12x2) = 0 Solving 480 + -180x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(40 + -15x + x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(40 + -15x + x2)' equal to zero and attempt to solve: Simplifying 40 + -15x + x2 = 0 Solving 40 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -15x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -15x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -15x + x2 = 0 + -40 -15x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -15x + x2 = -40 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -40 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -40 + 56.25 Combine like terms: -40 + 56.25 = 16.25 56.25 + -15x + x2 = 16.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + -7.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + -7.5 = 4.031128874 Simplifying x + -7.5 = 4.031128874 Reorder the terms: -7.5 + x = 4.031128874 Solving -7.5 + x = 4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 4.031128874 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 4.031128874 + 7.5 x = 4.031128874 + 7.5 Combine like terms: 4.031128874 + 7.5 = 11.531128874 x = 11.531128874 Simplifying x = 11.531128874Subproblem 2
x + -7.5 = -4.031128874 Simplifying x + -7.5 = -4.031128874 Reorder the terms: -7.5 + x = -4.031128874 Solving -7.5 + x = -4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -4.031128874 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -4.031128874 + 7.5 x = -4.031128874 + 7.5 Combine like terms: -4.031128874 + 7.5 = 3.468871126 x = 3.468871126 Simplifying x = 3.468871126Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.531128874, 3.468871126}Solution
x = {11.531128874, 3.468871126}
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