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Simplifying 4x2 + x + -15 = 180 Reorder the terms: -15 + x + 4x2 = 180 Solving -15 + x + 4x2 = 180 Solving for variable 'x'. Reorder the terms: -15 + -180 + x + 4x2 = 180 + -180 Combine like terms: -15 + -180 = -195 -195 + x + 4x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -195 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -48.75 + 0.25x + x2 = 0 Move the constant term to the right: Add '48.75' to each side of the equation. -48.75 + 0.25x + 48.75 + x2 = 0 + 48.75 Reorder the terms: -48.75 + 48.75 + 0.25x + x2 = 0 + 48.75 Combine like terms: -48.75 + 48.75 = 0.00 0.00 + 0.25x + x2 = 0 + 48.75 0.25x + x2 = 0 + 48.75 Combine like terms: 0 + 48.75 = 48.75 0.25x + x2 = 48.75 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. 0.25x + 0.25 + x2 = 48.75 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = 48.75 + 0.25 Combine like terms: 48.75 + 0.25 = 49 0.25 + 0.25x + x2 = 49 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 49 Calculate the square root of the right side: 7 Break this problem into two subproblems by setting (x + 0.5) equal to 7 and -7.Subproblem 1
x + 0.5 = 7 Simplifying x + 0.5 = 7 Reorder the terms: 0.5 + x = 7 Solving 0.5 + x = 7 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 = 7 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7 + -0.5 x = 7 + -0.5 Combine like terms: 7 + -0.5 = 6.5 x = 6.5 Simplifying x = 6.5Subproblem 2
x + 0.5 = -7 Simplifying x + 0.5 = -7 Reorder the terms: 0.5 + x = -7 Solving 0.5 + x = -7 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 = -7 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7 + -0.5 x = -7 + -0.5 Combine like terms: -7 + -0.5 = -7.5 x = -7.5 Simplifying x = -7.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.5, -7.5}
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