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Simplifying 2x2 + 2x + -1.5 = 15 Reorder the terms: -1.5 + 2x + 2x2 = 15 Solving -1.5 + 2x + 2x2 = 15 Solving for variable 'x'. Reorder the terms: -1.5 + -15 + 2x + 2x2 = 15 + -15 Combine like terms: -1.5 + -15 = -16.5 -16.5 + 2x + 2x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -16.5 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8.25 + x + x2 = 0 Move the constant term to the right: Add '8.25' to each side of the equation. -8.25 + x + 8.25 + x2 = 0 + 8.25 Reorder the terms: -8.25 + 8.25 + x + x2 = 0 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x + x2 = 0 + 8.25 x + x2 = 0 + 8.25 Combine like terms: 0 + 8.25 = 8.25 x + x2 = 8.25 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 8.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 8.25 + 0.25 Combine like terms: 8.25 + 0.25 = 8.5 1.25 + x2 = 8.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (x + 0.5) equal to 2.915475947 and -2.915475947.Subproblem 1
x + 0.5 = 2.915475947 Simplifying x + 0.5 = 2.915475947 Reorder the terms: 0.5 + x = 2.915475947 Solving 0.5 + x = 2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.915475947 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.915475947 + -0.5 x = 2.915475947 + -0.5 Combine like terms: 2.915475947 + -0.5 = 2.415475947 x = 2.415475947 Simplifying x = 2.415475947Subproblem 2
x + 0.5 = -2.915475947 Simplifying x + 0.5 = -2.915475947 Reorder the terms: 0.5 + x = -2.915475947 Solving 0.5 + x = -2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.915475947 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.915475947 + -0.5 x = -2.915475947 + -0.5 Combine like terms: -2.915475947 + -0.5 = -3.415475947 x = -3.415475947 Simplifying x = -3.415475947Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.415475947, -3.415475947}
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