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Simplifying (6x2 + -4x + 15) + (2x2 + 7x + -70) = 0 Reorder the terms: (15 + -4x + 6x2) + (2x2 + 7x + -70) = 0 Remove parenthesis around (15 + -4x + 6x2) 15 + -4x + 6x2 + (2x2 + 7x + -70) = 0 Reorder the terms: 15 + -4x + 6x2 + (-70 + 7x + 2x2) = 0 Remove parenthesis around (-70 + 7x + 2x2) 15 + -4x + 6x2 + -70 + 7x + 2x2 = 0 Reorder the terms: 15 + -70 + -4x + 7x + 6x2 + 2x2 = 0 Combine like terms: 15 + -70 = -55 -55 + -4x + 7x + 6x2 + 2x2 = 0 Combine like terms: -4x + 7x = 3x -55 + 3x + 6x2 + 2x2 = 0 Combine like terms: 6x2 + 2x2 = 8x2 -55 + 3x + 8x2 = 0 Solving -55 + 3x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -6.875 + 0.375x + x2 = 0 Move the constant term to the right: Add '6.875' to each side of the equation. -6.875 + 0.375x + 6.875 + x2 = 0 + 6.875 Reorder the terms: -6.875 + 6.875 + 0.375x + x2 = 0 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + 0.375x + x2 = 0 + 6.875 0.375x + x2 = 0 + 6.875 Combine like terms: 0 + 6.875 = 6.875 0.375x + x2 = 6.875 The x term is 0.375x. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375x + 0.03515625 + x2 = 6.875 + 0.03515625 Reorder the terms: 0.03515625 + 0.375x + x2 = 6.875 + 0.03515625 Combine like terms: 6.875 + 0.03515625 = 6.91015625 0.03515625 + 0.375x + x2 = 6.91015625 Factor a perfect square on the left side: (x + 0.1875)(x + 0.1875) = 6.91015625 Calculate the square root of the right side: 2.628717606 Break this problem into two subproblems by setting (x + 0.1875) equal to 2.628717606 and -2.628717606.Subproblem 1
x + 0.1875 = 2.628717606 Simplifying x + 0.1875 = 2.628717606 Reorder the terms: 0.1875 + x = 2.628717606 Solving 0.1875 + x = 2.628717606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 2.628717606 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 2.628717606 + -0.1875 x = 2.628717606 + -0.1875 Combine like terms: 2.628717606 + -0.1875 = 2.441217606 x = 2.441217606 Simplifying x = 2.441217606Subproblem 2
x + 0.1875 = -2.628717606 Simplifying x + 0.1875 = -2.628717606 Reorder the terms: 0.1875 + x = -2.628717606 Solving 0.1875 + x = -2.628717606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -2.628717606 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -2.628717606 + -0.1875 x = -2.628717606 + -0.1875 Combine like terms: -2.628717606 + -0.1875 = -2.816217606 x = -2.816217606 Simplifying x = -2.816217606Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.441217606, -2.816217606}
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