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Simplifying 53 = 2x2 + -15x + -36 Reorder the terms: 53 = -36 + -15x + 2x2 Solving 53 = -36 + -15x + 2x2 Solving for variable 'x'. Combine like terms: 53 + 36 = 89 89 + 15x + -2x2 = -36 + -15x + 2x2 + 36 + 15x + -2x2 Reorder the terms: 89 + 15x + -2x2 = -36 + 36 + -15x + 15x + 2x2 + -2x2 Combine like terms: -36 + 36 = 0 89 + 15x + -2x2 = 0 + -15x + 15x + 2x2 + -2x2 89 + 15x + -2x2 = -15x + 15x + 2x2 + -2x2 Combine like terms: -15x + 15x = 0 89 + 15x + -2x2 = 0 + 2x2 + -2x2 89 + 15x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 89 + 15x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -44.5 + -7.5x + x2 = 0 Move the constant term to the right: Add '44.5' to each side of the equation. -44.5 + -7.5x + 44.5 + x2 = 0 + 44.5 Reorder the terms: -44.5 + 44.5 + -7.5x + x2 = 0 + 44.5 Combine like terms: -44.5 + 44.5 = 0.0 0.0 + -7.5x + x2 = 0 + 44.5 -7.5x + x2 = 0 + 44.5 Combine like terms: 0 + 44.5 = 44.5 -7.5x + x2 = 44.5 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 44.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 44.5 + 14.0625 Combine like terms: 44.5 + 14.0625 = 58.5625 14.0625 + -7.5x + x2 = 58.5625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 58.5625 Calculate the square root of the right side: 7.652613933 Break this problem into two subproblems by setting (x + -3.75) equal to 7.652613933 and -7.652613933.Subproblem 1
x + -3.75 = 7.652613933 Simplifying x + -3.75 = 7.652613933 Reorder the terms: -3.75 + x = 7.652613933 Solving -3.75 + x = 7.652613933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 7.652613933 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 7.652613933 + 3.75 x = 7.652613933 + 3.75 Combine like terms: 7.652613933 + 3.75 = 11.402613933 x = 11.402613933 Simplifying x = 11.402613933Subproblem 2
x + -3.75 = -7.652613933 Simplifying x + -3.75 = -7.652613933 Reorder the terms: -3.75 + x = -7.652613933 Solving -3.75 + x = -7.652613933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -7.652613933 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -7.652613933 + 3.75 x = -7.652613933 + 3.75 Combine like terms: -7.652613933 + 3.75 = -3.902613933 x = -3.902613933 Simplifying x = -3.902613933Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.402613933, -3.902613933}
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