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Simplifying -294 + -110x + 4x2 = 450 Solving -294 + -110x + 4x2 = 450 Solving for variable 'x'. Reorder the terms: -294 + -450 + -110x + 4x2 = 450 + -450 Combine like terms: -294 + -450 = -744 -744 + -110x + 4x2 = 450 + -450 Combine like terms: 450 + -450 = 0 -744 + -110x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-372 + -55x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-372 + -55x + 2x2)' equal to zero and attempt to solve: Simplifying -372 + -55x + 2x2 = 0 Solving -372 + -55x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -186 + -27.5x + x2 = 0 Move the constant term to the right: Add '186' to each side of the equation. -186 + -27.5x + 186 + x2 = 0 + 186 Reorder the terms: -186 + 186 + -27.5x + x2 = 0 + 186 Combine like terms: -186 + 186 = 0 0 + -27.5x + x2 = 0 + 186 -27.5x + x2 = 0 + 186 Combine like terms: 0 + 186 = 186 -27.5x + x2 = 186 The x term is -27.5x. Take half its coefficient (-13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. -27.5x + 189.0625 + x2 = 186 + 189.0625 Reorder the terms: 189.0625 + -27.5x + x2 = 186 + 189.0625 Combine like terms: 186 + 189.0625 = 375.0625 189.0625 + -27.5x + x2 = 375.0625 Factor a perfect square on the left side: (x + -13.75)(x + -13.75) = 375.0625 Calculate the square root of the right side: 19.366530407 Break this problem into two subproblems by setting (x + -13.75) equal to 19.366530407 and -19.366530407.Subproblem 1
x + -13.75 = 19.366530407 Simplifying x + -13.75 = 19.366530407 Reorder the terms: -13.75 + x = 19.366530407 Solving -13.75 + x = 19.366530407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + x = 19.366530407 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = 19.366530407 + 13.75 x = 19.366530407 + 13.75 Combine like terms: 19.366530407 + 13.75 = 33.116530407 x = 33.116530407 Simplifying x = 33.116530407Subproblem 2
x + -13.75 = -19.366530407 Simplifying x + -13.75 = -19.366530407 Reorder the terms: -13.75 + x = -19.366530407 Solving -13.75 + x = -19.366530407 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + x = -19.366530407 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + x = -19.366530407 + 13.75 x = -19.366530407 + 13.75 Combine like terms: -19.366530407 + 13.75 = -5.616530407 x = -5.616530407 Simplifying x = -5.616530407Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.116530407, -5.616530407}Solution
x = {33.116530407, -5.616530407}
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