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Simplifying 0.5x2 + -0.5x + 7.473 = 100 Reorder the terms: 7.473 + -0.5x + 0.5x2 = 100 Solving 7.473 + -0.5x + 0.5x2 = 100 Solving for variable 'x'. Reorder the terms: 7.473 + -100 + -0.5x + 0.5x2 = 100 + -100 Combine like terms: 7.473 + -100 = -92.527 -92.527 + -0.5x + 0.5x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -92.527 + -0.5x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -185.054 + -1x + x2 = 0 Move the constant term to the right: Add '185.054' to each side of the equation. -185.054 + -1x + 185.054 + x2 = 0 + 185.054 Reorder the terms: -185.054 + 185.054 + -1x + x2 = 0 + 185.054 Combine like terms: -185.054 + 185.054 = 0.000 0.000 + -1x + x2 = 0 + 185.054 -1x + x2 = 0 + 185.054 Combine like terms: 0 + 185.054 = 185.054 -1x + x2 = 185.054 The x term is -1x. 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. -1x + 0.25 + x2 = 185.054 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 185.054 + 0.25 Combine like terms: 185.054 + 0.25 = 185.304 0.25 + -1x + x2 = 185.304 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 185.304 Calculate the square root of the right side: 13.612641184 Break this problem into two subproblems by setting (x + -0.5) equal to 13.612641184 and -13.612641184.Subproblem 1
x + -0.5 = 13.612641184 Simplifying x + -0.5 = 13.612641184 Reorder the terms: -0.5 + x = 13.612641184 Solving -0.5 + x = 13.612641184 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 = 13.612641184 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 13.612641184 + 0.5 x = 13.612641184 + 0.5 Combine like terms: 13.612641184 + 0.5 = 14.112641184 x = 14.112641184 Simplifying x = 14.112641184Subproblem 2
x + -0.5 = -13.612641184 Simplifying x + -0.5 = -13.612641184 Reorder the terms: -0.5 + x = -13.612641184 Solving -0.5 + x = -13.612641184 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 = -13.612641184 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -13.612641184 + 0.5 x = -13.612641184 + 0.5 Combine like terms: -13.612641184 + 0.5 = -13.112641184 x = -13.112641184 Simplifying x = -13.112641184Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.112641184, -13.112641184}
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