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Simplifying 3x(3x + 4) + -10 = -3x + 2(2x + 9) Reorder the terms: 3x(4 + 3x) + -10 = -3x + 2(2x + 9) (4 * 3x + 3x * 3x) + -10 = -3x + 2(2x + 9) (12x + 9x2) + -10 = -3x + 2(2x + 9) Reorder the terms: -10 + 12x + 9x2 = -3x + 2(2x + 9) Reorder the terms: -10 + 12x + 9x2 = -3x + 2(9 + 2x) -10 + 12x + 9x2 = -3x + (9 * 2 + 2x * 2) -10 + 12x + 9x2 = -3x + (18 + 4x) Reorder the terms: -10 + 12x + 9x2 = 18 + -3x + 4x Combine like terms: -3x + 4x = 1x -10 + 12x + 9x2 = 18 + 1x Solving -10 + 12x + 9x2 = 18 + 1x Solving for variable 'x'. Reorder the terms: -10 + -18 + 12x + -1x + 9x2 = 18 + 1x + -18 + -1x Combine like terms: -10 + -18 = -28 -28 + 12x + -1x + 9x2 = 18 + 1x + -18 + -1x Combine like terms: 12x + -1x = 11x -28 + 11x + 9x2 = 18 + 1x + -18 + -1x Reorder the terms: -28 + 11x + 9x2 = 18 + -18 + 1x + -1x Combine like terms: 18 + -18 = 0 -28 + 11x + 9x2 = 0 + 1x + -1x -28 + 11x + 9x2 = 1x + -1x Combine like terms: 1x + -1x = 0 -28 + 11x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.111111111 + 1.222222222x + x2 = 0 Move the constant term to the right: Add '3.111111111' to each side of the equation. -3.111111111 + 1.222222222x + 3.111111111 + x2 = 0 + 3.111111111 Reorder the terms: -3.111111111 + 3.111111111 + 1.222222222x + x2 = 0 + 3.111111111 Combine like terms: -3.111111111 + 3.111111111 = 0.000000000 0.000000000 + 1.222222222x + x2 = 0 + 3.111111111 1.222222222x + x2 = 0 + 3.111111111 Combine like terms: 0 + 3.111111111 = 3.111111111 1.222222222x + x2 = 3.111111111 The x term is 1.222222222x. Take half its coefficient (0.611111111). Square it (0.3734567900) and add it to both sides. Add '0.3734567900' to each side of the equation. 1.222222222x + 0.3734567900 + x2 = 3.111111111 + 0.3734567900 Reorder the terms: 0.3734567900 + 1.222222222x + x2 = 3.111111111 + 0.3734567900 Combine like terms: 3.111111111 + 0.3734567900 = 3.484567901 0.3734567900 + 1.222222222x + x2 = 3.484567901 Factor a perfect square on the left side: (x + 0.611111111)(x + 0.611111111) = 3.484567901 Calculate the square root of the right side: 1.866699735 Break this problem into two subproblems by setting (x + 0.611111111) equal to 1.866699735 and -1.866699735.Subproblem 1
x + 0.611111111 = 1.866699735 Simplifying x + 0.611111111 = 1.866699735 Reorder the terms: 0.611111111 + x = 1.866699735 Solving 0.611111111 + x = 1.866699735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + x = 1.866699735 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + x = 1.866699735 + -0.611111111 x = 1.866699735 + -0.611111111 Combine like terms: 1.866699735 + -0.611111111 = 1.255588624 x = 1.255588624 Simplifying x = 1.255588624Subproblem 2
x + 0.611111111 = -1.866699735 Simplifying x + 0.611111111 = -1.866699735 Reorder the terms: 0.611111111 + x = -1.866699735 Solving 0.611111111 + x = -1.866699735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.611111111' to each side of the equation. 0.611111111 + -0.611111111 + x = -1.866699735 + -0.611111111 Combine like terms: 0.611111111 + -0.611111111 = 0.000000000 0.000000000 + x = -1.866699735 + -0.611111111 x = -1.866699735 + -0.611111111 Combine like terms: -1.866699735 + -0.611111111 = -2.477810846 x = -2.477810846 Simplifying x = -2.477810846Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.255588624, -2.477810846}
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