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Simplifying -0.5x2 + 3x + 6 = -7 Reorder the terms: 6 + 3x + -0.5x2 = -7 Solving 6 + 3x + -0.5x2 = -7 Solving for variable 'x'. Reorder the terms: 6 + 7 + 3x + -0.5x2 = -7 + 7 Combine like terms: 6 + 7 = 13 13 + 3x + -0.5x2 = -7 + 7 Combine like terms: -7 + 7 = 0 13 + 3x + -0.5x2 = 0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -26 + -6x + x2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + -6x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + -6x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -6x + x2 = 0 + 26 -6x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 -6x + x2 = 26 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 26 + 9 Reorder the terms: 9 + -6x + x2 = 26 + 9 Combine like terms: 26 + 9 = 35 9 + -6x + x2 = 35 Factor a perfect square on the left side: (x + -3)(x + -3) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (x + -3) equal to 5.916079783 and -5.916079783.Subproblem 1
x + -3 = 5.916079783 Simplifying x + -3 = 5.916079783 Reorder the terms: -3 + x = 5.916079783 Solving -3 + x = 5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 5.916079783 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.916079783 + 3 x = 5.916079783 + 3 Combine like terms: 5.916079783 + 3 = 8.916079783 x = 8.916079783 Simplifying x = 8.916079783Subproblem 2
x + -3 = -5.916079783 Simplifying x + -3 = -5.916079783 Reorder the terms: -3 + x = -5.916079783 Solving -3 + x = -5.916079783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -5.916079783 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.916079783 + 3 x = -5.916079783 + 3 Combine like terms: -5.916079783 + 3 = -2.916079783 x = -2.916079783 Simplifying x = -2.916079783Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.916079783, -2.916079783}
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