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Simplifying 4x2 + -13x + 13 = 5x + 10 Reorder the terms: 13 + -13x + 4x2 = 5x + 10 Reorder the terms: 13 + -13x + 4x2 = 10 + 5x Solving 13 + -13x + 4x2 = 10 + 5x Solving for variable 'x'. Reorder the terms: 13 + -10 + -13x + -5x + 4x2 = 10 + 5x + -10 + -5x Combine like terms: 13 + -10 = 3 3 + -13x + -5x + 4x2 = 10 + 5x + -10 + -5x Combine like terms: -13x + -5x = -18x 3 + -18x + 4x2 = 10 + 5x + -10 + -5x Reorder the terms: 3 + -18x + 4x2 = 10 + -10 + 5x + -5x Combine like terms: 10 + -10 = 0 3 + -18x + 4x2 = 0 + 5x + -5x 3 + -18x + 4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 3 + -18x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + -4.5x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -4.5x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -4.5x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -4.5x + x2 = 0 + -0.75 -4.5x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -4.5x + x2 = -0.75 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -0.75 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -0.75 + 5.0625 Combine like terms: -0.75 + 5.0625 = 4.3125 5.0625 + -4.5x + x2 = 4.3125 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 4.3125 Calculate the square root of the right side: 2.076655966 Break this problem into two subproblems by setting (x + -2.25) equal to 2.076655966 and -2.076655966.Subproblem 1
x + -2.25 = 2.076655966 Simplifying x + -2.25 = 2.076655966 Reorder the terms: -2.25 + x = 2.076655966 Solving -2.25 + x = 2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 2.076655966 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 2.076655966 + 2.25 x = 2.076655966 + 2.25 Combine like terms: 2.076655966 + 2.25 = 4.326655966 x = 4.326655966 Simplifying x = 4.326655966Subproblem 2
x + -2.25 = -2.076655966 Simplifying x + -2.25 = -2.076655966 Reorder the terms: -2.25 + x = -2.076655966 Solving -2.25 + x = -2.076655966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -2.076655966 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -2.076655966 + 2.25 x = -2.076655966 + 2.25 Combine like terms: -2.076655966 + 2.25 = 0.173344034 x = 0.173344034 Simplifying x = 0.173344034Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.326655966, 0.173344034}
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