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Simplifying 2x2 + -15x = 35 Reorder the terms: -15x + 2x2 = 35 Solving -15x + 2x2 = 35 Solving for variable 'x'. Reorder the terms: -35 + -15x + 2x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + -15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -17.5 + -7.5x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -7.5x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -7.5x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -7.5x + x2 = 0 + 17.5 -7.5x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -7.5x + x2 = 17.5 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 = 17.5 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 17.5 + 14.0625 Combine like terms: 17.5 + 14.0625 = 31.5625 14.0625 + -7.5x + x2 = 31.5625 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 31.5625 Calculate the square root of the right side: 5.618051264 Break this problem into two subproblems by setting (x + -3.75) equal to 5.618051264 and -5.618051264.Subproblem 1
x + -3.75 = 5.618051264 Simplifying x + -3.75 = 5.618051264 Reorder the terms: -3.75 + x = 5.618051264 Solving -3.75 + x = 5.618051264 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 = 5.618051264 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 5.618051264 + 3.75 x = 5.618051264 + 3.75 Combine like terms: 5.618051264 + 3.75 = 9.368051264 x = 9.368051264 Simplifying x = 9.368051264Subproblem 2
x + -3.75 = -5.618051264 Simplifying x + -3.75 = -5.618051264 Reorder the terms: -3.75 + x = -5.618051264 Solving -3.75 + x = -5.618051264 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 = -5.618051264 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -5.618051264 + 3.75 x = -5.618051264 + 3.75 Combine like terms: -5.618051264 + 3.75 = -1.868051264 x = -1.868051264 Simplifying x = -1.868051264Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.368051264, -1.868051264}
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