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Simplifying 46 = 4x2 + 10x Reorder the terms: 46 = 10x + 4x2 Solving 46 = 10x + 4x2 Solving for variable 'x'. Reorder the terms: 46 + -10x + -4x2 = 10x + -10x + 4x2 + -4x2 Combine like terms: 10x + -10x = 0 46 + -10x + -4x2 = 0 + 4x2 + -4x2 46 + -10x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 46 + -10x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(23 + -5x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(23 + -5x + -2x2)' equal to zero and attempt to solve: Simplifying 23 + -5x + -2x2 = 0 Solving 23 + -5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -11.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + 2.5x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + 2.5x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + 2.5x + x2 = 0 + 11.5 2.5x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 2.5x + x2 = 11.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 11.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 11.5 + 1.5625 Combine like terms: 11.5 + 1.5625 = 13.0625 1.5625 + 2.5x + x2 = 13.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 13.0625 Calculate the square root of the right side: 3.614208074 Break this problem into two subproblems by setting (x + 1.25) equal to 3.614208074 and -3.614208074.Subproblem 1
x + 1.25 = 3.614208074 Simplifying x + 1.25 = 3.614208074 Reorder the terms: 1.25 + x = 3.614208074 Solving 1.25 + x = 3.614208074 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 3.614208074 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 3.614208074 + -1.25 x = 3.614208074 + -1.25 Combine like terms: 3.614208074 + -1.25 = 2.364208074 x = 2.364208074 Simplifying x = 2.364208074Subproblem 2
x + 1.25 = -3.614208074 Simplifying x + 1.25 = -3.614208074 Reorder the terms: 1.25 + x = -3.614208074 Solving 1.25 + x = -3.614208074 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -3.614208074 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -3.614208074 + -1.25 x = -3.614208074 + -1.25 Combine like terms: -3.614208074 + -1.25 = -4.864208074 x = -4.864208074 Simplifying x = -4.864208074Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.364208074, -4.864208074}Solution
x = {2.364208074, -4.864208074}
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