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Simplifying 146 = 5x + x2 Solving 146 = 5x + x2 Solving for variable 'x'. Reorder the terms: 146 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 146 + -5x + -1x2 = 0 + x2 + -1x2 146 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 146 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -146 + 5x + x2 = 0 Move the constant term to the right: Add '146' to each side of the equation. -146 + 5x + 146 + x2 = 0 + 146 Reorder the terms: -146 + 146 + 5x + x2 = 0 + 146 Combine like terms: -146 + 146 = 0 0 + 5x + x2 = 0 + 146 5x + x2 = 0 + 146 Combine like terms: 0 + 146 = 146 5x + x2 = 146 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 146 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 146 + 6.25 Combine like terms: 146 + 6.25 = 152.25 6.25 + 5x + x2 = 152.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 152.25 Calculate the square root of the right side: 12.338962679 Break this problem into two subproblems by setting (x + 2.5) equal to 12.338962679 and -12.338962679.Subproblem 1
x + 2.5 = 12.338962679 Simplifying x + 2.5 = 12.338962679 Reorder the terms: 2.5 + x = 12.338962679 Solving 2.5 + x = 12.338962679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 12.338962679 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 12.338962679 + -2.5 x = 12.338962679 + -2.5 Combine like terms: 12.338962679 + -2.5 = 9.838962679 x = 9.838962679 Simplifying x = 9.838962679Subproblem 2
x + 2.5 = -12.338962679 Simplifying x + 2.5 = -12.338962679 Reorder the terms: 2.5 + x = -12.338962679 Solving 2.5 + x = -12.338962679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -12.338962679 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -12.338962679 + -2.5 x = -12.338962679 + -2.5 Combine like terms: -12.338962679 + -2.5 = -14.838962679 x = -14.838962679 Simplifying x = -14.838962679Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.838962679, -14.838962679}
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