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Simplifying 10x2 + -38x + 26 = 0 Reorder the terms: 26 + -38x + 10x2 = 0 Solving 26 + -38x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(13 + -19x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(13 + -19x + 5x2)' equal to zero and attempt to solve: Simplifying 13 + -19x + 5x2 = 0 Solving 13 + -19x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.6 + -3.8x + x2 = 0 Move the constant term to the right: Add '-2.6' to each side of the equation. 2.6 + -3.8x + -2.6 + x2 = 0 + -2.6 Reorder the terms: 2.6 + -2.6 + -3.8x + x2 = 0 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + -3.8x + x2 = 0 + -2.6 -3.8x + x2 = 0 + -2.6 Combine like terms: 0 + -2.6 = -2.6 -3.8x + x2 = -2.6 The x term is -3.8x. Take half its coefficient (-1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. -3.8x + 3.61 + x2 = -2.6 + 3.61 Reorder the terms: 3.61 + -3.8x + x2 = -2.6 + 3.61 Combine like terms: -2.6 + 3.61 = 1.01 3.61 + -3.8x + x2 = 1.01 Factor a perfect square on the left side: (x + -1.9)(x + -1.9) = 1.01 Calculate the square root of the right side: 1.004987562 Break this problem into two subproblems by setting (x + -1.9) equal to 1.004987562 and -1.004987562.Subproblem 1
x + -1.9 = 1.004987562 Simplifying x + -1.9 = 1.004987562 Reorder the terms: -1.9 + x = 1.004987562 Solving -1.9 + x = 1.004987562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = 1.004987562 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = 1.004987562 + 1.9 x = 1.004987562 + 1.9 Combine like terms: 1.004987562 + 1.9 = 2.904987562 x = 2.904987562 Simplifying x = 2.904987562Subproblem 2
x + -1.9 = -1.004987562 Simplifying x + -1.9 = -1.004987562 Reorder the terms: -1.9 + x = -1.004987562 Solving -1.9 + x = -1.004987562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.9' to each side of the equation. -1.9 + 1.9 + x = -1.004987562 + 1.9 Combine like terms: -1.9 + 1.9 = 0.0 0.0 + x = -1.004987562 + 1.9 x = -1.004987562 + 1.9 Combine like terms: -1.004987562 + 1.9 = 0.895012438 x = 0.895012438 Simplifying x = 0.895012438Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.904987562, 0.895012438}Solution
x = {2.904987562, 0.895012438}
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