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Simplifying x + x + 25 + 30 + -58x * 78x = 93 Reorder the terms for easier multiplication: x + x + 25 + 30 + -58 * 78x * x = 93 Multiply -58 * 78 x + x + 25 + 30 + -4524x * x = 93 Multiply x * x x + x + 25 + 30 + -4524x2 = 93 Reorder the terms: 25 + 30 + x + x + -4524x2 = 93 Combine like terms: 25 + 30 = 55 55 + x + x + -4524x2 = 93 Combine like terms: x + x = 2x 55 + 2x + -4524x2 = 93 Solving 55 + 2x + -4524x2 = 93 Solving for variable 'x'. Reorder the terms: 55 + -93 + 2x + -4524x2 = 93 + -93 Combine like terms: 55 + -93 = -38 -38 + 2x + -4524x2 = 93 + -93 Combine like terms: 93 + -93 = 0 -38 + 2x + -4524x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-19 + x + -2262x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + x + -2262x2)' equal to zero and attempt to solve: Simplifying -19 + x + -2262x2 = 0 Solving -19 + x + -2262x2 = 0 Begin completing the square. Divide all terms by -2262 the coefficient of the squared term: Divide each side by '-2262'. 0.008399646331 + -0.0004420866490x + x2 = 0 Move the constant term to the right: Add '-0.008399646331' to each side of the equation. 0.008399646331 + -0.0004420866490x + -0.008399646331 + x2 = 0 + -0.008399646331 Reorder the terms: 0.008399646331 + -0.008399646331 + -0.0004420866490x + x2 = 0 + -0.008399646331 Combine like terms: 0.008399646331 + -0.008399646331 = 0.000000000000 0.000000000000 + -0.0004420866490x + x2 = 0 + -0.008399646331 -0.0004420866490x + x2 = 0 + -0.008399646331 Combine like terms: 0 + -0.008399646331 = -0.008399646331 -0.0004420866490x + x2 = -0.008399646331 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.0004420866490x + 0.25 + x2 = -0.008399646331 + 0.25 Reorder the terms: 0.25 + -0.0004420866490x + x2 = -0.008399646331 + 0.25 Combine like terms: -0.008399646331 + 0.25 = 0.241600353669 0.25 + -0.0004420866490x + x2 = 0.241600353669 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.241600353669 Calculate the square root of the right side: 0.491528589 Break this problem into two subproblems by setting (x + 0.5) equal to 0.491528589 and -0.491528589.Subproblem 1
x + 0.5 = 0.491528589 Simplifying x + 0.5 = 0.491528589 Reorder the terms: 0.5 + x = 0.491528589 Solving 0.5 + x = 0.491528589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.491528589 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.491528589 + -0.5 x = 0.491528589 + -0.5 Combine like terms: 0.491528589 + -0.5 = -0.008471411 x = -0.008471411 Simplifying x = -0.008471411Subproblem 2
x + 0.5 = -0.491528589 Simplifying x + 0.5 = -0.491528589 Reorder the terms: 0.5 + x = -0.491528589 Solving 0.5 + x = -0.491528589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.491528589 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.491528589 + -0.5 x = -0.491528589 + -0.5 Combine like terms: -0.491528589 + -0.5 = -0.991528589 x = -0.991528589 Simplifying x = -0.991528589Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.008471411, -0.991528589}Solution
x = {-0.008471411, -0.991528589}
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