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Simplifying 0 = 15x2 + -36x + -24 Reorder the terms: 0 = -24 + -36x + 15x2 Solving 0 = -24 + -36x + 15x2 Solving for variable 'x'. Combine like terms: 0 + 24 = 24 24 + 36x + -15x2 = -24 + -36x + 15x2 + 24 + 36x + -15x2 Reorder the terms: 24 + 36x + -15x2 = -24 + 24 + -36x + 36x + 15x2 + -15x2 Combine like terms: -24 + 24 = 0 24 + 36x + -15x2 = 0 + -36x + 36x + 15x2 + -15x2 24 + 36x + -15x2 = -36x + 36x + 15x2 + -15x2 Combine like terms: -36x + 36x = 0 24 + 36x + -15x2 = 0 + 15x2 + -15x2 24 + 36x + -15x2 = 15x2 + -15x2 Combine like terms: 15x2 + -15x2 = 0 24 + 36x + -15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(8 + 12x + -5x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(8 + 12x + -5x2)' equal to zero and attempt to solve: Simplifying 8 + 12x + -5x2 = 0 Solving 8 + 12x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.6 + -2.4x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -2.4x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + -2.4x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -2.4x + x2 = 0 + 1.6 -2.4x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 -2.4x + x2 = 1.6 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 1.6 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 1.6 + 1.44 Combine like terms: 1.6 + 1.44 = 3.04 1.44 + -2.4x + x2 = 3.04 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 3.04 Calculate the square root of the right side: 1.743559577 Break this problem into two subproblems by setting (x + -1.2) equal to 1.743559577 and -1.743559577.Subproblem 1
x + -1.2 = 1.743559577 Simplifying x + -1.2 = 1.743559577 Reorder the terms: -1.2 + x = 1.743559577 Solving -1.2 + x = 1.743559577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 1.743559577 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 1.743559577 + 1.2 x = 1.743559577 + 1.2 Combine like terms: 1.743559577 + 1.2 = 2.943559577 x = 2.943559577 Simplifying x = 2.943559577Subproblem 2
x + -1.2 = -1.743559577 Simplifying x + -1.2 = -1.743559577 Reorder the terms: -1.2 + x = -1.743559577 Solving -1.2 + x = -1.743559577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -1.743559577 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -1.743559577 + 1.2 x = -1.743559577 + 1.2 Combine like terms: -1.743559577 + 1.2 = -0.543559577 x = -0.543559577 Simplifying x = -0.543559577Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.943559577, -0.543559577}Solution
x = {2.943559577, -0.543559577}
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