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Simplifying 4x * 4x + -10x + -390 = 0 Reorder the terms for easier multiplication: 4 * 4x * x + -10x + -390 = 0 Multiply 4 * 4 16x * x + -10x + -390 = 0 Multiply x * x 16x2 + -10x + -390 = 0 Reorder the terms: -390 + -10x + 16x2 = 0 Solving -390 + -10x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-195 + -5x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-195 + -5x + 8x2)' equal to zero and attempt to solve: Simplifying -195 + -5x + 8x2 = 0 Solving -195 + -5x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -24.375 + -0.625x + x2 = 0 Move the constant term to the right: Add '24.375' to each side of the equation. -24.375 + -0.625x + 24.375 + x2 = 0 + 24.375 Reorder the terms: -24.375 + 24.375 + -0.625x + x2 = 0 + 24.375 Combine like terms: -24.375 + 24.375 = 0.000 0.000 + -0.625x + x2 = 0 + 24.375 -0.625x + x2 = 0 + 24.375 Combine like terms: 0 + 24.375 = 24.375 -0.625x + x2 = 24.375 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 24.375 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 24.375 + 0.09765625 Combine like terms: 24.375 + 0.09765625 = 24.47265625 0.09765625 + -0.625x + x2 = 24.47265625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 24.47265625 Calculate the square root of the right side: 4.946984561 Break this problem into two subproblems by setting (x + -0.3125) equal to 4.946984561 and -4.946984561.Subproblem 1
x + -0.3125 = 4.946984561 Simplifying x + -0.3125 = 4.946984561 Reorder the terms: -0.3125 + x = 4.946984561 Solving -0.3125 + x = 4.946984561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 4.946984561 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 4.946984561 + 0.3125 x = 4.946984561 + 0.3125 Combine like terms: 4.946984561 + 0.3125 = 5.259484561 x = 5.259484561 Simplifying x = 5.259484561Subproblem 2
x + -0.3125 = -4.946984561 Simplifying x + -0.3125 = -4.946984561 Reorder the terms: -0.3125 + x = -4.946984561 Solving -0.3125 + x = -4.946984561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -4.946984561 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -4.946984561 + 0.3125 x = -4.946984561 + 0.3125 Combine like terms: -4.946984561 + 0.3125 = -4.634484561 x = -4.634484561 Simplifying x = -4.634484561Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.259484561, -4.634484561}Solution
x = {5.259484561, -4.634484561}
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