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Simplifying (2x2 + -7x + 13) + (2x2 + 9x + -42) = 0 Reorder the terms: (13 + -7x + 2x2) + (2x2 + 9x + -42) = 0 Remove parenthesis around (13 + -7x + 2x2) 13 + -7x + 2x2 + (2x2 + 9x + -42) = 0 Reorder the terms: 13 + -7x + 2x2 + (-42 + 9x + 2x2) = 0 Remove parenthesis around (-42 + 9x + 2x2) 13 + -7x + 2x2 + -42 + 9x + 2x2 = 0 Reorder the terms: 13 + -42 + -7x + 9x + 2x2 + 2x2 = 0 Combine like terms: 13 + -42 = -29 -29 + -7x + 9x + 2x2 + 2x2 = 0 Combine like terms: -7x + 9x = 2x -29 + 2x + 2x2 + 2x2 = 0 Combine like terms: 2x2 + 2x2 = 4x2 -29 + 2x + 4x2 = 0 Solving -29 + 2x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.25 + 0.5x + x2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + 0.5x + 7.25 + x2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + 0.5x + x2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + 0.5x + x2 = 0 + 7.25 0.5x + x2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 0.5x + x2 = 7.25 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 7.25 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 7.25 + 0.0625 Combine like terms: 7.25 + 0.0625 = 7.3125 0.0625 + 0.5x + x2 = 7.3125 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 7.3125 Calculate the square root of the right side: 2.704163457 Break this problem into two subproblems by setting (x + 0.25) equal to 2.704163457 and -2.704163457.Subproblem 1
x + 0.25 = 2.704163457 Simplifying x + 0.25 = 2.704163457 Reorder the terms: 0.25 + x = 2.704163457 Solving 0.25 + x = 2.704163457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 2.704163457 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.704163457 + -0.25 x = 2.704163457 + -0.25 Combine like terms: 2.704163457 + -0.25 = 2.454163457 x = 2.454163457 Simplifying x = 2.454163457Subproblem 2
x + 0.25 = -2.704163457 Simplifying x + 0.25 = -2.704163457 Reorder the terms: 0.25 + x = -2.704163457 Solving 0.25 + x = -2.704163457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -2.704163457 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.704163457 + -0.25 x = -2.704163457 + -0.25 Combine like terms: -2.704163457 + -0.25 = -2.954163457 x = -2.954163457 Simplifying x = -2.954163457Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.454163457, -2.954163457}
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