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Simplifying 10x2 + -38x + 24 = 13x Reorder the terms: 24 + -38x + 10x2 = 13x Solving 24 + -38x + 10x2 = 13x Solving for variable 'x'. Reorder the terms: 24 + -38x + -13x + 10x2 = 13x + -13x Combine like terms: -38x + -13x = -51x 24 + -51x + 10x2 = 13x + -13x Combine like terms: 13x + -13x = 0 24 + -51x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 2.4 + -5.1x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -5.1x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -5.1x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -5.1x + x2 = 0 + -2.4 -5.1x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -5.1x + x2 = -2.4 The x term is -5.1x. Take half its coefficient (-2.55). Square it (6.5025) and add it to both sides. Add '6.5025' to each side of the equation. -5.1x + 6.5025 + x2 = -2.4 + 6.5025 Reorder the terms: 6.5025 + -5.1x + x2 = -2.4 + 6.5025 Combine like terms: -2.4 + 6.5025 = 4.1025 6.5025 + -5.1x + x2 = 4.1025 Factor a perfect square on the left side: (x + -2.55)(x + -2.55) = 4.1025 Calculate the square root of the right side: 2.02546291 Break this problem into two subproblems by setting (x + -2.55) equal to 2.02546291 and -2.02546291.Subproblem 1
x + -2.55 = 2.02546291 Simplifying x + -2.55 = 2.02546291 Reorder the terms: -2.55 + x = 2.02546291 Solving -2.55 + x = 2.02546291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.55' to each side of the equation. -2.55 + 2.55 + x = 2.02546291 + 2.55 Combine like terms: -2.55 + 2.55 = 0.00 0.00 + x = 2.02546291 + 2.55 x = 2.02546291 + 2.55 Combine like terms: 2.02546291 + 2.55 = 4.57546291 x = 4.57546291 Simplifying x = 4.57546291Subproblem 2
x + -2.55 = -2.02546291 Simplifying x + -2.55 = -2.02546291 Reorder the terms: -2.55 + x = -2.02546291 Solving -2.55 + x = -2.02546291 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.55' to each side of the equation. -2.55 + 2.55 + x = -2.02546291 + 2.55 Combine like terms: -2.55 + 2.55 = 0.00 0.00 + x = -2.02546291 + 2.55 x = -2.02546291 + 2.55 Combine like terms: -2.02546291 + 2.55 = 0.52453709 x = 0.52453709 Simplifying x = 0.52453709Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.57546291, 0.52453709}
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