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Simplifying 3x * 3x + -21 = 2x * 2x + -4x Reorder the terms for easier multiplication: 3 * 3x * x + -21 = 2x * 2x + -4x Multiply 3 * 3 9x * x + -21 = 2x * 2x + -4x Multiply x * x 9x2 + -21 = 2x * 2x + -4x Reorder the terms: -21 + 9x2 = 2x * 2x + -4x Reorder the terms for easier multiplication: -21 + 9x2 = 2 * 2x * x + -4x Multiply 2 * 2 -21 + 9x2 = 4x * x + -4x Multiply x * x -21 + 9x2 = 4x2 + -4x Reorder the terms: -21 + 9x2 = -4x + 4x2 Solving -21 + 9x2 = -4x + 4x2 Solving for variable 'x'. Reorder the terms: -21 + 4x + 9x2 + -4x2 = -4x + 4x2 + 4x + -4x2 Combine like terms: 9x2 + -4x2 = 5x2 -21 + 4x + 5x2 = -4x + 4x2 + 4x + -4x2 Reorder the terms: -21 + 4x + 5x2 = -4x + 4x + 4x2 + -4x2 Combine like terms: -4x + 4x = 0 -21 + 4x + 5x2 = 0 + 4x2 + -4x2 -21 + 4x + 5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -21 + 4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.2 + 0.8x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + 0.8x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + 0.8x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + 0.8x + x2 = 0 + 4.2 0.8x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 0.8x + x2 = 4.2 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 4.2 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 4.2 + 0.16 Combine like terms: 4.2 + 0.16 = 4.36 0.16 + 0.8x + x2 = 4.36 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 4.36 Calculate the square root of the right side: 2.088061302 Break this problem into two subproblems by setting (x + 0.4) equal to 2.088061302 and -2.088061302.Subproblem 1
x + 0.4 = 2.088061302 Simplifying x + 0.4 = 2.088061302 Reorder the terms: 0.4 + x = 2.088061302 Solving 0.4 + x = 2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 2.088061302 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 2.088061302 + -0.4 x = 2.088061302 + -0.4 Combine like terms: 2.088061302 + -0.4 = 1.688061302 x = 1.688061302 Simplifying x = 1.688061302Subproblem 2
x + 0.4 = -2.088061302 Simplifying x + 0.4 = -2.088061302 Reorder the terms: 0.4 + x = -2.088061302 Solving 0.4 + x = -2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -2.088061302 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -2.088061302 + -0.4 x = -2.088061302 + -0.4 Combine like terms: -2.088061302 + -0.4 = -2.488061302 x = -2.488061302 Simplifying x = -2.488061302Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.688061302, -2.488061302}
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