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Simplifying -2x2 + 8x + 9 = 0 Reorder the terms: 9 + 8x + -2x2 = 0 Solving 9 + 8x + -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'. -4.5 + -4x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -4x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -4x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -4x + x2 = 0 + 4.5 -4x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -4x + x2 = 4.5 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 4.5 + 4 Reorder the terms: 4 + -4x + x2 = 4.5 + 4 Combine like terms: 4.5 + 4 = 8.5 4 + -4x + x2 = 8.5 Factor a perfect square on the left side: (x + -2)(x + -2) = 8.5 Calculate the square root of the right side: 2.915475947 Break this problem into two subproblems by setting (x + -2) equal to 2.915475947 and -2.915475947.Subproblem 1
x + -2 = 2.915475947 Simplifying x + -2 = 2.915475947 Reorder the terms: -2 + x = 2.915475947 Solving -2 + x = 2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.915475947 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.915475947 + 2 x = 2.915475947 + 2 Combine like terms: 2.915475947 + 2 = 4.915475947 x = 4.915475947 Simplifying x = 4.915475947Subproblem 2
x + -2 = -2.915475947 Simplifying x + -2 = -2.915475947 Reorder the terms: -2 + x = -2.915475947 Solving -2 + x = -2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.915475947 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.915475947 + 2 x = -2.915475947 + 2 Combine like terms: -2.915475947 + 2 = -0.915475947 x = -0.915475947 Simplifying x = -0.915475947Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.915475947, -0.915475947}
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