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Simplifying 2x2 + 6x + -7 = 11.5 Reorder the terms: -7 + 6x + 2x2 = 11.5 Solving -7 + 6x + 2x2 = 11.5 Solving for variable 'x'. Reorder the terms: -7 + -11.5 + 6x + 2x2 = 11.5 + -11.5 Combine like terms: -7 + -11.5 = -18.5 -18.5 + 6x + 2x2 = 11.5 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 -18.5 + 6x + 2x2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -9.25 + 3x + x2 = 0.0 Move the constant term to the right: Add '9.25' to each side of the equation. -9.25 + 3x + 9.25 + x2 = 0.0 + 9.25 Reorder the terms: -9.25 + 9.25 + 3x + x2 = 0.0 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + 3x + x2 = 0.0 + 9.25 3x + x2 = 0.0 + 9.25 Combine like terms: 0.0 + 9.25 = 9.25 3x + x2 = 9.25 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 9.25 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 9.25 + 2.25 Combine like terms: 9.25 + 2.25 = 11.5 2.25 + 3x + x2 = 11.5 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (x + 1.5) equal to 3.391164992 and -3.391164992.Subproblem 1
x + 1.5 = 3.391164992 Simplifying x + 1.5 = 3.391164992 Reorder the terms: 1.5 + x = 3.391164992 Solving 1.5 + x = 3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 3.391164992 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.391164992 + -1.5 x = 3.391164992 + -1.5 Combine like terms: 3.391164992 + -1.5 = 1.891164992 x = 1.891164992 Simplifying x = 1.891164992Subproblem 2
x + 1.5 = -3.391164992 Simplifying x + 1.5 = -3.391164992 Reorder the terms: 1.5 + x = -3.391164992 Solving 1.5 + x = -3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -3.391164992 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.391164992 + -1.5 x = -3.391164992 + -1.5 Combine like terms: -3.391164992 + -1.5 = -4.891164992 x = -4.891164992 Simplifying x = -4.891164992Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.891164992, -4.891164992}
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