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Simplifying 3(8x(3x)) + 3x = 3x + 9x + 47 Remove parenthesis around (3x) 3(8x * 3x) + 3x = 3x + 9x + 47 Reorder the terms for easier multiplication: 3(8 * 3x * x) + 3x = 3x + 9x + 47 Multiply 8 * 3 3(24x * x) + 3x = 3x + 9x + 47 Multiply x * x 3(24x2) + 3x = 3x + 9x + 47 Remove parenthesis around (24x2) 3 * 24x2 + 3x = 3x + 9x + 47 Multiply 3 * 24 72x2 + 3x = 3x + 9x + 47 Reorder the terms: 3x + 72x2 = 3x + 9x + 47 Reorder the terms: 3x + 72x2 = 47 + 3x + 9x Combine like terms: 3x + 9x = 12x 3x + 72x2 = 47 + 12x Solving 3x + 72x2 = 47 + 12x Solving for variable 'x'. Reorder the terms: -47 + 3x + -12x + 72x2 = 47 + 12x + -47 + -12x Combine like terms: 3x + -12x = -9x -47 + -9x + 72x2 = 47 + 12x + -47 + -12x Reorder the terms: -47 + -9x + 72x2 = 47 + -47 + 12x + -12x Combine like terms: 47 + -47 = 0 -47 + -9x + 72x2 = 0 + 12x + -12x -47 + -9x + 72x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -47 + -9x + 72x2 = 0 Begin completing the square. Divide all terms by 72 the coefficient of the squared term: Divide each side by '72'. -0.6527777778 + -0.125x + x2 = 0 Move the constant term to the right: Add '0.6527777778' to each side of the equation. -0.6527777778 + -0.125x + 0.6527777778 + x2 = 0 + 0.6527777778 Reorder the terms: -0.6527777778 + 0.6527777778 + -0.125x + x2 = 0 + 0.6527777778 Combine like terms: -0.6527777778 + 0.6527777778 = 0.0000000000 0.0000000000 + -0.125x + x2 = 0 + 0.6527777778 -0.125x + x2 = 0 + 0.6527777778 Combine like terms: 0 + 0.6527777778 = 0.6527777778 -0.125x + x2 = 0.6527777778 The x term is -0.125x. Take half its coefficient (-0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. -0.125x + 0.00390625 + x2 = 0.6527777778 + 0.00390625 Reorder the terms: 0.00390625 + -0.125x + x2 = 0.6527777778 + 0.00390625 Combine like terms: 0.6527777778 + 0.00390625 = 0.6566840278 0.00390625 + -0.125x + x2 = 0.6566840278 Factor a perfect square on the left side: (x + -0.0625)(x + -0.0625) = 0.6566840278 Calculate the square root of the right side: 0.810360431 Break this problem into two subproblems by setting (x + -0.0625) equal to 0.810360431 and -0.810360431.Subproblem 1
x + -0.0625 = 0.810360431 Simplifying x + -0.0625 = 0.810360431 Reorder the terms: -0.0625 + x = 0.810360431 Solving -0.0625 + x = 0.810360431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = 0.810360431 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = 0.810360431 + 0.0625 x = 0.810360431 + 0.0625 Combine like terms: 0.810360431 + 0.0625 = 0.872860431 x = 0.872860431 Simplifying x = 0.872860431Subproblem 2
x + -0.0625 = -0.810360431 Simplifying x + -0.0625 = -0.810360431 Reorder the terms: -0.0625 + x = -0.810360431 Solving -0.0625 + x = -0.810360431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0625' to each side of the equation. -0.0625 + 0.0625 + x = -0.810360431 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + x = -0.810360431 + 0.0625 x = -0.810360431 + 0.0625 Combine like terms: -0.810360431 + 0.0625 = -0.747860431 x = -0.747860431 Simplifying x = -0.747860431Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.872860431, -0.747860431}
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