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Simplifying 26x2 + -20x = 24 Reorder the terms: -20x + 26x2 = 24 Solving -20x + 26x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + -20x + 26x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -20x + 26x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -10x + 13x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + -10x + 13x2)' equal to zero and attempt to solve: Simplifying -12 + -10x + 13x2 = 0 Solving -12 + -10x + 13x2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. -0.9230769231 + -0.7692307692x + x2 = 0 Move the constant term to the right: Add '0.9230769231' to each side of the equation. -0.9230769231 + -0.7692307692x + 0.9230769231 + x2 = 0 + 0.9230769231 Reorder the terms: -0.9230769231 + 0.9230769231 + -0.7692307692x + x2 = 0 + 0.9230769231 Combine like terms: -0.9230769231 + 0.9230769231 = 0.0000000000 0.0000000000 + -0.7692307692x + x2 = 0 + 0.9230769231 -0.7692307692x + x2 = 0 + 0.9230769231 Combine like terms: 0 + 0.9230769231 = 0.9230769231 -0.7692307692x + x2 = 0.9230769231 The x term is -0.7692307692x. Take half its coefficient (-0.3846153846). Square it (0.1479289941) and add it to both sides. Add '0.1479289941' to each side of the equation. -0.7692307692x + 0.1479289941 + x2 = 0.9230769231 + 0.1479289941 Reorder the terms: 0.1479289941 + -0.7692307692x + x2 = 0.9230769231 + 0.1479289941 Combine like terms: 0.9230769231 + 0.1479289941 = 1.0710059172 0.1479289941 + -0.7692307692x + x2 = 1.0710059172 Factor a perfect square on the left side: (x + -0.3846153846)(x + -0.3846153846) = 1.0710059172 Calculate the square root of the right side: 1.034894157 Break this problem into two subproblems by setting (x + -0.3846153846) equal to 1.034894157 and -1.034894157.Subproblem 1
x + -0.3846153846 = 1.034894157 Simplifying x + -0.3846153846 = 1.034894157 Reorder the terms: -0.3846153846 + x = 1.034894157 Solving -0.3846153846 + x = 1.034894157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3846153846' to each side of the equation. -0.3846153846 + 0.3846153846 + x = 1.034894157 + 0.3846153846 Combine like terms: -0.3846153846 + 0.3846153846 = 0.0000000000 0.0000000000 + x = 1.034894157 + 0.3846153846 x = 1.034894157 + 0.3846153846 Combine like terms: 1.034894157 + 0.3846153846 = 1.4195095416 x = 1.4195095416 Simplifying x = 1.4195095416Subproblem 2
x + -0.3846153846 = -1.034894157 Simplifying x + -0.3846153846 = -1.034894157 Reorder the terms: -0.3846153846 + x = -1.034894157 Solving -0.3846153846 + x = -1.034894157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3846153846' to each side of the equation. -0.3846153846 + 0.3846153846 + x = -1.034894157 + 0.3846153846 Combine like terms: -0.3846153846 + 0.3846153846 = 0.0000000000 0.0000000000 + x = -1.034894157 + 0.3846153846 x = -1.034894157 + 0.3846153846 Combine like terms: -1.034894157 + 0.3846153846 = -0.6502787724 x = -0.6502787724 Simplifying x = -0.6502787724Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4195095416, -0.6502787724}Solution
x = {1.4195095416, -0.6502787724}
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