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Simplifying 7x2 + -4x + 29 + 2x2 + 6x = 86 Reorder the terms: 29 + -4x + 6x + 7x2 + 2x2 = 86 Combine like terms: -4x + 6x = 2x 29 + 2x + 7x2 + 2x2 = 86 Combine like terms: 7x2 + 2x2 = 9x2 29 + 2x + 9x2 = 86 Solving 29 + 2x + 9x2 = 86 Solving for variable 'x'. Reorder the terms: 29 + -86 + 2x + 9x2 = 86 + -86 Combine like terms: 29 + -86 = -57 -57 + 2x + 9x2 = 86 + -86 Combine like terms: 86 + -86 = 0 -57 + 2x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -6.333333333 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '6.333333333' to each side of the equation. -6.333333333 + 0.2222222222x + 6.333333333 + x2 = 0 + 6.333333333 Reorder the terms: -6.333333333 + 6.333333333 + 0.2222222222x + x2 = 0 + 6.333333333 Combine like terms: -6.333333333 + 6.333333333 = 0.000000000 0.000000000 + 0.2222222222x + x2 = 0 + 6.333333333 0.2222222222x + x2 = 0 + 6.333333333 Combine like terms: 0 + 6.333333333 = 6.333333333 0.2222222222x + x2 = 6.333333333 The x term is 0.2222222222x. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222x + 0.01234567901 + x2 = 6.333333333 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = 6.333333333 + 0.01234567901 Combine like terms: 6.333333333 + 0.01234567901 = 6.34567901201 0.01234567901 + 0.2222222222x + x2 = 6.34567901201 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = 6.34567901201 Calculate the square root of the right side: 2.519063122 Break this problem into two subproblems by setting (x + 0.1111111111) equal to 2.519063122 and -2.519063122.Subproblem 1
x + 0.1111111111 = 2.519063122 Simplifying x + 0.1111111111 = 2.519063122 Reorder the terms: 0.1111111111 + x = 2.519063122 Solving 0.1111111111 + x = 2.519063122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = 2.519063122 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 2.519063122 + -0.1111111111 x = 2.519063122 + -0.1111111111 Combine like terms: 2.519063122 + -0.1111111111 = 2.4079520109 x = 2.4079520109 Simplifying x = 2.4079520109Subproblem 2
x + 0.1111111111 = -2.519063122 Simplifying x + 0.1111111111 = -2.519063122 Reorder the terms: 0.1111111111 + x = -2.519063122 Solving 0.1111111111 + x = -2.519063122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = -2.519063122 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -2.519063122 + -0.1111111111 x = -2.519063122 + -0.1111111111 Combine like terms: -2.519063122 + -0.1111111111 = -2.6301742331 x = -2.6301742331 Simplifying x = -2.6301742331Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.4079520109, -2.6301742331}
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