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Simplifying 0.25x2 + 2x + -1 = 31.5 Reorder the terms: -1 + 2x + 0.25x2 = 31.5 Solving -1 + 2x + 0.25x2 = 31.5 Solving for variable 'x'. Reorder the terms: -1 + -31.5 + 2x + 0.25x2 = 31.5 + -31.5 Combine like terms: -1 + -31.5 = -32.5 -32.5 + 2x + 0.25x2 = 31.5 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 -32.5 + 2x + 0.25x2 = 0.0 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -130 + 8x + x2 = 0 Move the constant term to the right: Add '130' to each side of the equation. -130 + 8x + 130 + x2 = 0 + 130 Reorder the terms: -130 + 130 + 8x + x2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + 8x + x2 = 0 + 130 8x + x2 = 0 + 130 Combine like terms: 0 + 130 = 130 8x + x2 = 130 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 130 + 16 Reorder the terms: 16 + 8x + x2 = 130 + 16 Combine like terms: 130 + 16 = 146 16 + 8x + x2 = 146 Factor a perfect square on the left side: (x + 4)(x + 4) = 146 Calculate the square root of the right side: 12.083045974 Break this problem into two subproblems by setting (x + 4) equal to 12.083045974 and -12.083045974.Subproblem 1
x + 4 = 12.083045974 Simplifying x + 4 = 12.083045974 Reorder the terms: 4 + x = 12.083045974 Solving 4 + x = 12.083045974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 12.083045974 + -4 Combine like terms: 4 + -4 = 0 0 + x = 12.083045974 + -4 x = 12.083045974 + -4 Combine like terms: 12.083045974 + -4 = 8.083045974 x = 8.083045974 Simplifying x = 8.083045974Subproblem 2
x + 4 = -12.083045974 Simplifying x + 4 = -12.083045974 Reorder the terms: 4 + x = -12.083045974 Solving 4 + x = -12.083045974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -12.083045974 + -4 Combine like terms: 4 + -4 = 0 0 + x = -12.083045974 + -4 x = -12.083045974 + -4 Combine like terms: -12.083045974 + -4 = -16.083045974 x = -16.083045974 Simplifying x = -16.083045974Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.083045974, -16.083045974}
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