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Simplifying 15 + -2x2 + -6x = 0 Reorder the terms: 15 + -6x + -2x2 = 0 Solving 15 + -6x + -2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -7.5 + 3x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 3x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 3x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 3x + x2 = 0 + 7.5 3x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 3x + x2 = 7.5 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 = 7.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 7.5 + 2.25 Combine like terms: 7.5 + 2.25 = 9.75 2.25 + 3x + x2 = 9.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 9.75 Calculate the square root of the right side: 3.122498999 Break this problem into two subproblems by setting (x + 1.5) equal to 3.122498999 and -3.122498999.Subproblem 1
x + 1.5 = 3.122498999 Simplifying x + 1.5 = 3.122498999 Reorder the terms: 1.5 + x = 3.122498999 Solving 1.5 + x = 3.122498999 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 = 3.122498999 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.122498999 + -1.5 x = 3.122498999 + -1.5 Combine like terms: 3.122498999 + -1.5 = 1.622498999 x = 1.622498999 Simplifying x = 1.622498999Subproblem 2
x + 1.5 = -3.122498999 Simplifying x + 1.5 = -3.122498999 Reorder the terms: 1.5 + x = -3.122498999 Solving 1.5 + x = -3.122498999 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 = -3.122498999 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.122498999 + -1.5 x = -3.122498999 + -1.5 Combine like terms: -3.122498999 + -1.5 = -4.622498999 x = -4.622498999 Simplifying x = -4.622498999Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.622498999, -4.622498999}
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