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Simplifying 148 = 2x2 + -7x Reorder the terms: 148 = -7x + 2x2 Solving 148 = -7x + 2x2 Solving for variable 'x'. Reorder the terms: 148 + 7x + -2x2 = -7x + 7x + 2x2 + -2x2 Combine like terms: -7x + 7x = 0 148 + 7x + -2x2 = 0 + 2x2 + -2x2 148 + 7x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 148 + 7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -74 + -3.5x + x2 = 0 Move the constant term to the right: Add '74' to each side of the equation. -74 + -3.5x + 74 + x2 = 0 + 74 Reorder the terms: -74 + 74 + -3.5x + x2 = 0 + 74 Combine like terms: -74 + 74 = 0 0 + -3.5x + x2 = 0 + 74 -3.5x + x2 = 0 + 74 Combine like terms: 0 + 74 = 74 -3.5x + x2 = 74 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 74 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 74 + 3.0625 Combine like terms: 74 + 3.0625 = 77.0625 3.0625 + -3.5x + x2 = 77.0625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 77.0625 Calculate the square root of the right side: 8.778524933 Break this problem into two subproblems by setting (x + -1.75) equal to 8.778524933 and -8.778524933.Subproblem 1
x + -1.75 = 8.778524933 Simplifying x + -1.75 = 8.778524933 Reorder the terms: -1.75 + x = 8.778524933 Solving -1.75 + x = 8.778524933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 8.778524933 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 8.778524933 + 1.75 x = 8.778524933 + 1.75 Combine like terms: 8.778524933 + 1.75 = 10.528524933 x = 10.528524933 Simplifying x = 10.528524933Subproblem 2
x + -1.75 = -8.778524933 Simplifying x + -1.75 = -8.778524933 Reorder the terms: -1.75 + x = -8.778524933 Solving -1.75 + x = -8.778524933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -8.778524933 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -8.778524933 + 1.75 x = -8.778524933 + 1.75 Combine like terms: -8.778524933 + 1.75 = -7.028524933 x = -7.028524933 Simplifying x = -7.028524933Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.528524933, -7.028524933}
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