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Simplifying (6x2 + -4) + (x2 + 4x + -10) = 0 Reorder the terms: (-4 + 6x2) + (x2 + 4x + -10) = 0 Remove parenthesis around (-4 + 6x2) -4 + 6x2 + (x2 + 4x + -10) = 0 Reorder the terms: -4 + 6x2 + (-10 + 4x + x2) = 0 Remove parenthesis around (-10 + 4x + x2) -4 + 6x2 + -10 + 4x + x2 = 0 Reorder the terms: -4 + -10 + 4x + 6x2 + x2 = 0 Combine like terms: -4 + -10 = -14 -14 + 4x + 6x2 + x2 = 0 Combine like terms: 6x2 + x2 = 7x2 -14 + 4x + 7x2 = 0 Solving -14 + 4x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.5714285714x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 0.5714285714x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.5714285714x + x2 = 0 + 2 0.5714285714x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 0.5714285714x + x2 = 2 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = 2 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 2 + 0.08163265305 Combine like terms: 2 + 0.08163265305 = 2.08163265305 0.08163265305 + 0.5714285714x + x2 = 2.08163265305 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 2.08163265305 Calculate the square root of the right side: 1.44278642 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 1.44278642 and -1.44278642.Subproblem 1
x + 0.2857142857 = 1.44278642 Simplifying x + 0.2857142857 = 1.44278642 Reorder the terms: 0.2857142857 + x = 1.44278642 Solving 0.2857142857 + x = 1.44278642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 1.44278642 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 1.44278642 + -0.2857142857 x = 1.44278642 + -0.2857142857 Combine like terms: 1.44278642 + -0.2857142857 = 1.1570721343 x = 1.1570721343 Simplifying x = 1.1570721343Subproblem 2
x + 0.2857142857 = -1.44278642 Simplifying x + 0.2857142857 = -1.44278642 Reorder the terms: 0.2857142857 + x = -1.44278642 Solving 0.2857142857 + x = -1.44278642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -1.44278642 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -1.44278642 + -0.2857142857 x = -1.44278642 + -0.2857142857 Combine like terms: -1.44278642 + -0.2857142857 = -1.7285007057 x = -1.7285007057 Simplifying x = -1.7285007057Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1570721343, -1.7285007057}
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