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Simplifying x2 + 4x + -7 + 8x2 + 9x + -7 = 0 Reorder the terms: -7 + -7 + 4x + 9x + x2 + 8x2 = 0 Combine like terms: -7 + -7 = -14 -14 + 4x + 9x + x2 + 8x2 = 0 Combine like terms: 4x + 9x = 13x -14 + 13x + x2 + 8x2 = 0 Combine like terms: x2 + 8x2 = 9x2 -14 + 13x + 9x2 = 0 Solving -14 + 13x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.555555556 + 1.444444444x + x2 = 0 Move the constant term to the right: Add '1.555555556' to each side of the equation. -1.555555556 + 1.444444444x + 1.555555556 + x2 = 0 + 1.555555556 Reorder the terms: -1.555555556 + 1.555555556 + 1.444444444x + x2 = 0 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + 1.444444444x + x2 = 0 + 1.555555556 1.444444444x + x2 = 0 + 1.555555556 Combine like terms: 0 + 1.555555556 = 1.555555556 1.444444444x + x2 = 1.555555556 The x term is 1.444444444x. Take half its coefficient (0.722222222). Square it (0.5216049380) and add it to both sides. Add '0.5216049380' to each side of the equation. 1.444444444x + 0.5216049380 + x2 = 1.555555556 + 0.5216049380 Reorder the terms: 0.5216049380 + 1.444444444x + x2 = 1.555555556 + 0.5216049380 Combine like terms: 1.555555556 + 0.5216049380 = 2.077160494 0.5216049380 + 1.444444444x + x2 = 2.077160494 Factor a perfect square on the left side: (x + 0.722222222)(x + 0.722222222) = 2.077160494 Calculate the square root of the right side: 1.441235752 Break this problem into two subproblems by setting (x + 0.722222222) equal to 1.441235752 and -1.441235752.Subproblem 1
x + 0.722222222 = 1.441235752 Simplifying x + 0.722222222 = 1.441235752 Reorder the terms: 0.722222222 + x = 1.441235752 Solving 0.722222222 + x = 1.441235752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.722222222' to each side of the equation. 0.722222222 + -0.722222222 + x = 1.441235752 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = 1.441235752 + -0.722222222 x = 1.441235752 + -0.722222222 Combine like terms: 1.441235752 + -0.722222222 = 0.71901353 x = 0.71901353 Simplifying x = 0.71901353Subproblem 2
x + 0.722222222 = -1.441235752 Simplifying x + 0.722222222 = -1.441235752 Reorder the terms: 0.722222222 + x = -1.441235752 Solving 0.722222222 + x = -1.441235752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.722222222' to each side of the equation. 0.722222222 + -0.722222222 + x = -1.441235752 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = -1.441235752 + -0.722222222 x = -1.441235752 + -0.722222222 Combine like terms: -1.441235752 + -0.722222222 = -2.163457974 x = -2.163457974 Simplifying x = -2.163457974Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.71901353, -2.163457974}
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