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Simplifying 3x * 3x + -8x + 5 = 5x * 5x Reorder the terms for easier multiplication: 3 * 3x * x + -8x + 5 = 5x * 5x Multiply 3 * 3 9x * x + -8x + 5 = 5x * 5x Multiply x * x 9x2 + -8x + 5 = 5x * 5x Reorder the terms: 5 + -8x + 9x2 = 5x * 5x Reorder the terms for easier multiplication: 5 + -8x + 9x2 = 5 * 5x * x Multiply 5 * 5 5 + -8x + 9x2 = 25x * x Multiply x * x 5 + -8x + 9x2 = 25x2 Solving 5 + -8x + 9x2 = 25x2 Solving for variable 'x'. Combine like terms: 9x2 + -25x2 = -16x2 5 + -8x + -16x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 5 + -8x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.3125 + 0.5x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + 0.5x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + 0.5x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + 0.5x + x2 = 0 + 0.3125 0.5x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 0.5x + x2 = 0.3125 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 0.3125 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 0.3125 + 0.0625 Combine like terms: 0.3125 + 0.0625 = 0.375 0.0625 + 0.5x + x2 = 0.375 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 0.375 Calculate the square root of the right side: 0.612372436 Break this problem into two subproblems by setting (x + 0.25) equal to 0.612372436 and -0.612372436.Subproblem 1
x + 0.25 = 0.612372436 Simplifying x + 0.25 = 0.612372436 Reorder the terms: 0.25 + x = 0.612372436 Solving 0.25 + x = 0.612372436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 0.612372436 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 0.612372436 + -0.25 x = 0.612372436 + -0.25 Combine like terms: 0.612372436 + -0.25 = 0.362372436 x = 0.362372436 Simplifying x = 0.362372436Subproblem 2
x + 0.25 = -0.612372436 Simplifying x + 0.25 = -0.612372436 Reorder the terms: 0.25 + x = -0.612372436 Solving 0.25 + x = -0.612372436 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -0.612372436 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -0.612372436 + -0.25 x = -0.612372436 + -0.25 Combine like terms: -0.612372436 + -0.25 = -0.862372436 x = -0.862372436 Simplifying x = -0.862372436Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.362372436, -0.862372436}
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