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Simplifying (7x2 + -6x + 25) + (5x2 + 8x + -58) = 0 Reorder the terms: (25 + -6x + 7x2) + (5x2 + 8x + -58) = 0 Remove parenthesis around (25 + -6x + 7x2) 25 + -6x + 7x2 + (5x2 + 8x + -58) = 0 Reorder the terms: 25 + -6x + 7x2 + (-58 + 8x + 5x2) = 0 Remove parenthesis around (-58 + 8x + 5x2) 25 + -6x + 7x2 + -58 + 8x + 5x2 = 0 Reorder the terms: 25 + -58 + -6x + 8x + 7x2 + 5x2 = 0 Combine like terms: 25 + -58 = -33 -33 + -6x + 8x + 7x2 + 5x2 = 0 Combine like terms: -6x + 8x = 2x -33 + 2x + 7x2 + 5x2 = 0 Combine like terms: 7x2 + 5x2 = 12x2 -33 + 2x + 12x2 = 0 Solving -33 + 2x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -2.75 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + 0.1666666667x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + 0.1666666667x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + 0.1666666667x + x2 = 0 + 2.75 0.1666666667x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 0.1666666667x + x2 = 2.75 The x term is 0.1666666667x. Take half its coefficient (0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. 0.1666666667x + 0.006944444447 + x2 = 2.75 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 2.75 + 0.006944444447 Combine like terms: 2.75 + 0.006944444447 = 2.756944444447 0.006944444447 + 0.1666666667x + x2 = 2.756944444447 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 2.756944444447 Calculate the square root of the right side: 1.660404904 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 1.660404904 and -1.660404904.Subproblem 1
x + 0.08333333335 = 1.660404904 Simplifying x + 0.08333333335 = 1.660404904 Reorder the terms: 0.08333333335 + x = 1.660404904 Solving 0.08333333335 + x = 1.660404904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = 1.660404904 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 1.660404904 + -0.08333333335 x = 1.660404904 + -0.08333333335 Combine like terms: 1.660404904 + -0.08333333335 = 1.57707157065 x = 1.57707157065 Simplifying x = 1.57707157065Subproblem 2
x + 0.08333333335 = -1.660404904 Simplifying x + 0.08333333335 = -1.660404904 Reorder the terms: 0.08333333335 + x = -1.660404904 Solving 0.08333333335 + x = -1.660404904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = -1.660404904 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -1.660404904 + -0.08333333335 x = -1.660404904 + -0.08333333335 Combine like terms: -1.660404904 + -0.08333333335 = -1.74373823735 x = -1.74373823735 Simplifying x = -1.74373823735Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.57707157065, -1.74373823735}
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