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Simplifying 53x3 + -10x2 + -8x = 0 Reorder the terms: -8x + -10x2 + 53x3 = 0 Solving -8x + -10x2 + 53x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-8 + -10x + 53x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-8 + -10x + 53x2)' equal to zero and attempt to solve: Simplifying -8 + -10x + 53x2 = 0 Solving -8 + -10x + 53x2 = 0 Begin completing the square. Divide all terms by 53 the coefficient of the squared term: Divide each side by '53'. -0.1509433962 + -0.1886792453x + x2 = 0 Move the constant term to the right: Add '0.1509433962' to each side of the equation. -0.1509433962 + -0.1886792453x + 0.1509433962 + x2 = 0 + 0.1509433962 Reorder the terms: -0.1509433962 + 0.1509433962 + -0.1886792453x + x2 = 0 + 0.1509433962 Combine like terms: -0.1509433962 + 0.1509433962 = 0.0000000000 0.0000000000 + -0.1886792453x + x2 = 0 + 0.1509433962 -0.1886792453x + x2 = 0 + 0.1509433962 Combine like terms: 0 + 0.1509433962 = 0.1509433962 -0.1886792453x + x2 = 0.1509433962 The x term is -0.1886792453x. Take half its coefficient (-0.09433962265). Square it (0.008899964402) and add it to both sides. Add '0.008899964402' to each side of the equation. -0.1886792453x + 0.008899964402 + x2 = 0.1509433962 + 0.008899964402 Reorder the terms: 0.008899964402 + -0.1886792453x + x2 = 0.1509433962 + 0.008899964402 Combine like terms: 0.1509433962 + 0.008899964402 = 0.159843360602 0.008899964402 + -0.1886792453x + x2 = 0.159843360602 Factor a perfect square on the left side: (x + -0.09433962265)(x + -0.09433962265) = 0.159843360602 Calculate the square root of the right side: 0.399804153 Break this problem into two subproblems by setting (x + -0.09433962265) equal to 0.399804153 and -0.399804153.Subproblem 1
x + -0.09433962265 = 0.399804153 Simplifying x + -0.09433962265 = 0.399804153 Reorder the terms: -0.09433962265 + x = 0.399804153 Solving -0.09433962265 + x = 0.399804153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09433962265' to each side of the equation. -0.09433962265 + 0.09433962265 + x = 0.399804153 + 0.09433962265 Combine like terms: -0.09433962265 + 0.09433962265 = 0.00000000000 0.00000000000 + x = 0.399804153 + 0.09433962265 x = 0.399804153 + 0.09433962265 Combine like terms: 0.399804153 + 0.09433962265 = 0.49414377565 x = 0.49414377565 Simplifying x = 0.49414377565Subproblem 2
x + -0.09433962265 = -0.399804153 Simplifying x + -0.09433962265 = -0.399804153 Reorder the terms: -0.09433962265 + x = -0.399804153 Solving -0.09433962265 + x = -0.399804153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.09433962265' to each side of the equation. -0.09433962265 + 0.09433962265 + x = -0.399804153 + 0.09433962265 Combine like terms: -0.09433962265 + 0.09433962265 = 0.00000000000 0.00000000000 + x = -0.399804153 + 0.09433962265 x = -0.399804153 + 0.09433962265 Combine like terms: -0.399804153 + 0.09433962265 = -0.30546453035 x = -0.30546453035 Simplifying x = -0.30546453035Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.49414377565, -0.30546453035}Solution
x = {0, 0.49414377565, -0.30546453035}
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