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Simplifying 2x2 + -12 + -1 = -7x + 6 Reorder the terms: -12 + -1 + 2x2 = -7x + 6 Combine like terms: -12 + -1 = -13 -13 + 2x2 = -7x + 6 Reorder the terms: -13 + 2x2 = 6 + -7x Solving -13 + 2x2 = 6 + -7x Solving for variable 'x'. Reorder the terms: -13 + -6 + 7x + 2x2 = 6 + -7x + -6 + 7x Combine like terms: -13 + -6 = -19 -19 + 7x + 2x2 = 6 + -7x + -6 + 7x Reorder the terms: -19 + 7x + 2x2 = 6 + -6 + -7x + 7x Combine like terms: 6 + -6 = 0 -19 + 7x + 2x2 = 0 + -7x + 7x -19 + 7x + 2x2 = -7x + 7x Combine like terms: -7x + 7x = 0 -19 + 7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.5 + 3.5x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + 3.5x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + 3.5x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + 3.5x + x2 = 0 + 9.5 3.5x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 3.5x + x2 = 9.5 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 = 9.5 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 9.5 + 3.0625 Combine like terms: 9.5 + 3.0625 = 12.5625 3.0625 + 3.5x + x2 = 12.5625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (x + 1.75) equal to 3.54436172 and -3.54436172.Subproblem 1
x + 1.75 = 3.54436172 Simplifying x + 1.75 = 3.54436172 Reorder the terms: 1.75 + x = 3.54436172 Solving 1.75 + x = 3.54436172 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 = 3.54436172 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 3.54436172 + -1.75 x = 3.54436172 + -1.75 Combine like terms: 3.54436172 + -1.75 = 1.79436172 x = 1.79436172 Simplifying x = 1.79436172Subproblem 2
x + 1.75 = -3.54436172 Simplifying x + 1.75 = -3.54436172 Reorder the terms: 1.75 + x = -3.54436172 Solving 1.75 + x = -3.54436172 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 = -3.54436172 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -3.54436172 + -1.75 x = -3.54436172 + -1.75 Combine like terms: -3.54436172 + -1.75 = -5.29436172 x = -5.29436172 Simplifying x = -5.29436172Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.79436172, -5.29436172}
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