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Simplifying 2x2 + -48x = 10 Reorder the terms: -48x + 2x2 = 10 Solving -48x + 2x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + -48x + 2x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -48x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -24x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -24x + x2)' equal to zero and attempt to solve: Simplifying -5 + -24x + x2 = 0 Solving -5 + -24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -24x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -24x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -24x + x2 = 0 + 5 -24x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -24x + x2 = 5 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 5 + 144 Reorder the terms: 144 + -24x + x2 = 5 + 144 Combine like terms: 5 + 144 = 149 144 + -24x + x2 = 149 Factor a perfect square on the left side: (x + -12)(x + -12) = 149 Calculate the square root of the right side: 12.206555616 Break this problem into two subproblems by setting (x + -12) equal to 12.206555616 and -12.206555616.Subproblem 1
x + -12 = 12.206555616 Simplifying x + -12 = 12.206555616 Reorder the terms: -12 + x = 12.206555616 Solving -12 + x = 12.206555616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 12.206555616 + 12 Combine like terms: -12 + 12 = 0 0 + x = 12.206555616 + 12 x = 12.206555616 + 12 Combine like terms: 12.206555616 + 12 = 24.206555616 x = 24.206555616 Simplifying x = 24.206555616Subproblem 2
x + -12 = -12.206555616 Simplifying x + -12 = -12.206555616 Reorder the terms: -12 + x = -12.206555616 Solving -12 + x = -12.206555616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -12.206555616 + 12 Combine like terms: -12 + 12 = 0 0 + x = -12.206555616 + 12 x = -12.206555616 + 12 Combine like terms: -12.206555616 + 12 = -0.206555616 x = -0.206555616 Simplifying x = -0.206555616Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.206555616, -0.206555616}Solution
x = {24.206555616, -0.206555616}
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