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Simplifying x2 + 3 = 12 + -10x2 + 10x Reorder the terms: 3 + x2 = 12 + -10x2 + 10x Reorder the terms: 3 + x2 = 12 + 10x + -10x2 Solving 3 + x2 = 12 + 10x + -10x2 Solving for variable 'x'. Reorder the terms: 3 + -12 + -10x + x2 + 10x2 = 12 + 10x + -10x2 + -12 + -10x + 10x2 Combine like terms: 3 + -12 = -9 -9 + -10x + x2 + 10x2 = 12 + 10x + -10x2 + -12 + -10x + 10x2 Combine like terms: x2 + 10x2 = 11x2 -9 + -10x + 11x2 = 12 + 10x + -10x2 + -12 + -10x + 10x2 Reorder the terms: -9 + -10x + 11x2 = 12 + -12 + 10x + -10x + -10x2 + 10x2 Combine like terms: 12 + -12 = 0 -9 + -10x + 11x2 = 0 + 10x + -10x + -10x2 + 10x2 -9 + -10x + 11x2 = 10x + -10x + -10x2 + 10x2 Combine like terms: 10x + -10x = 0 -9 + -10x + 11x2 = 0 + -10x2 + 10x2 -9 + -10x + 11x2 = -10x2 + 10x2 Combine like terms: -10x2 + 10x2 = 0 -9 + -10x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.8181818182 + -0.9090909091x + x2 = 0 Move the constant term to the right: Add '0.8181818182' to each side of the equation. -0.8181818182 + -0.9090909091x + 0.8181818182 + x2 = 0 + 0.8181818182 Reorder the terms: -0.8181818182 + 0.8181818182 + -0.9090909091x + x2 = 0 + 0.8181818182 Combine like terms: -0.8181818182 + 0.8181818182 = 0.0000000000 0.0000000000 + -0.9090909091x + x2 = 0 + 0.8181818182 -0.9090909091x + x2 = 0 + 0.8181818182 Combine like terms: 0 + 0.8181818182 = 0.8181818182 -0.9090909091x + x2 = 0.8181818182 The x term is -0.9090909091x. Take half its coefficient (-0.4545454546). Square it (0.2066115703) and add it to both sides. Add '0.2066115703' to each side of the equation. -0.9090909091x + 0.2066115703 + x2 = 0.8181818182 + 0.2066115703 Reorder the terms: 0.2066115703 + -0.9090909091x + x2 = 0.8181818182 + 0.2066115703 Combine like terms: 0.8181818182 + 0.2066115703 = 1.0247933885 0.2066115703 + -0.9090909091x + x2 = 1.0247933885 Factor a perfect square on the left side: (x + -0.4545454546)(x + -0.4545454546) = 1.0247933885 Calculate the square root of the right side: 1.012320793 Break this problem into two subproblems by setting (x + -0.4545454546) equal to 1.012320793 and -1.012320793.Subproblem 1
x + -0.4545454546 = 1.012320793 Simplifying x + -0.4545454546 = 1.012320793 Reorder the terms: -0.4545454546 + x = 1.012320793 Solving -0.4545454546 + x = 1.012320793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4545454546' to each side of the equation. -0.4545454546 + 0.4545454546 + x = 1.012320793 + 0.4545454546 Combine like terms: -0.4545454546 + 0.4545454546 = 0.0000000000 0.0000000000 + x = 1.012320793 + 0.4545454546 x = 1.012320793 + 0.4545454546 Combine like terms: 1.012320793 + 0.4545454546 = 1.4668662476 x = 1.4668662476 Simplifying x = 1.4668662476Subproblem 2
x + -0.4545454546 = -1.012320793 Simplifying x + -0.4545454546 = -1.012320793 Reorder the terms: -0.4545454546 + x = -1.012320793 Solving -0.4545454546 + x = -1.012320793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4545454546' to each side of the equation. -0.4545454546 + 0.4545454546 + x = -1.012320793 + 0.4545454546 Combine like terms: -0.4545454546 + 0.4545454546 = 0.0000000000 0.0000000000 + x = -1.012320793 + 0.4545454546 x = -1.012320793 + 0.4545454546 Combine like terms: -1.012320793 + 0.4545454546 = -0.5577753384 x = -0.5577753384 Simplifying x = -0.5577753384Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4668662476, -0.5577753384}
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