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Simplifying (3x)(3x) + 20x = 7 Remove parenthesis around (3x) 3x(3x) + 20x = 7 Remove parenthesis around (3x) 3x * 3x + 20x = 7 Reorder the terms for easier multiplication: 3 * 3x * x + 20x = 7 Multiply 3 * 3 9x * x + 20x = 7 Multiply x * x 9x2 + 20x = 7 Reorder the terms: 20x + 9x2 = 7 Solving 20x + 9x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 20x + 9x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 20x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.7777777778 + 2.222222222x + x2 = 0 Move the constant term to the right: Add '0.7777777778' to each side of the equation. -0.7777777778 + 2.222222222x + 0.7777777778 + x2 = 0 + 0.7777777778 Reorder the terms: -0.7777777778 + 0.7777777778 + 2.222222222x + x2 = 0 + 0.7777777778 Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000 0.0000000000 + 2.222222222x + x2 = 0 + 0.7777777778 2.222222222x + x2 = 0 + 0.7777777778 Combine like terms: 0 + 0.7777777778 = 0.7777777778 2.222222222x + x2 = 0.7777777778 The x term is 2.222222222x. Take half its coefficient (1.111111111). Square it (1.234567901) and add it to both sides. Add '1.234567901' to each side of the equation. 2.222222222x + 1.234567901 + x2 = 0.7777777778 + 1.234567901 Reorder the terms: 1.234567901 + 2.222222222x + x2 = 0.7777777778 + 1.234567901 Combine like terms: 0.7777777778 + 1.234567901 = 2.0123456788 1.234567901 + 2.222222222x + x2 = 2.0123456788 Factor a perfect square on the left side: (x + 1.111111111)(x + 1.111111111) = 2.0123456788 Calculate the square root of the right side: 1.418571704 Break this problem into two subproblems by setting (x + 1.111111111) equal to 1.418571704 and -1.418571704.Subproblem 1
x + 1.111111111 = 1.418571704 Simplifying x + 1.111111111 = 1.418571704 Reorder the terms: 1.111111111 + x = 1.418571704 Solving 1.111111111 + x = 1.418571704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.111111111' to each side of the equation. 1.111111111 + -1.111111111 + x = 1.418571704 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + x = 1.418571704 + -1.111111111 x = 1.418571704 + -1.111111111 Combine like terms: 1.418571704 + -1.111111111 = 0.307460593 x = 0.307460593 Simplifying x = 0.307460593Subproblem 2
x + 1.111111111 = -1.418571704 Simplifying x + 1.111111111 = -1.418571704 Reorder the terms: 1.111111111 + x = -1.418571704 Solving 1.111111111 + x = -1.418571704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.111111111' to each side of the equation. 1.111111111 + -1.111111111 + x = -1.418571704 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + x = -1.418571704 + -1.111111111 x = -1.418571704 + -1.111111111 Combine like terms: -1.418571704 + -1.111111111 = -2.529682815 x = -2.529682815 Simplifying x = -2.529682815Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.307460593, -2.529682815}
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