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Simplifying 1x + 3x(5x) = 15 Remove parenthesis around (5x) 1x + 3x * 5x = 15 Reorder the terms for easier multiplication: 1x + 3 * 5x * x = 15 Multiply 3 * 5 1x + 15x * x = 15 Multiply x * x 1x + 15x2 = 15 Solving 1x + 15x2 = 15 Solving for variable 'x'. Reorder the terms: -15 + 1x + 15x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + 1x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1 + 0.06666666667x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.06666666667x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.06666666667x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.06666666667x + x2 = 0 + 1 0.06666666667x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.06666666667x + x2 = 1 The x term is 0.06666666667x. Take half its coefficient (0.03333333334). Square it (0.001111111112) and add it to both sides. Add '0.001111111112' to each side of the equation. 0.06666666667x + 0.001111111112 + x2 = 1 + 0.001111111112 Reorder the terms: 0.001111111112 + 0.06666666667x + x2 = 1 + 0.001111111112 Combine like terms: 1 + 0.001111111112 = 1.001111111112 0.001111111112 + 0.06666666667x + x2 = 1.001111111112 Factor a perfect square on the left side: (x + 0.03333333334)(x + 0.03333333334) = 1.001111111112 Calculate the square root of the right side: 1.000555401 Break this problem into two subproblems by setting (x + 0.03333333334) equal to 1.000555401 and -1.000555401.Subproblem 1
x + 0.03333333334 = 1.000555401 Simplifying x + 0.03333333334 = 1.000555401 Reorder the terms: 0.03333333334 + x = 1.000555401 Solving 0.03333333334 + x = 1.000555401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03333333334' to each side of the equation. 0.03333333334 + -0.03333333334 + x = 1.000555401 + -0.03333333334 Combine like terms: 0.03333333334 + -0.03333333334 = 0.00000000000 0.00000000000 + x = 1.000555401 + -0.03333333334 x = 1.000555401 + -0.03333333334 Combine like terms: 1.000555401 + -0.03333333334 = 0.96722206766 x = 0.96722206766 Simplifying x = 0.96722206766Subproblem 2
x + 0.03333333334 = -1.000555401 Simplifying x + 0.03333333334 = -1.000555401 Reorder the terms: 0.03333333334 + x = -1.000555401 Solving 0.03333333334 + x = -1.000555401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03333333334' to each side of the equation. 0.03333333334 + -0.03333333334 + x = -1.000555401 + -0.03333333334 Combine like terms: 0.03333333334 + -0.03333333334 = 0.00000000000 0.00000000000 + x = -1.000555401 + -0.03333333334 x = -1.000555401 + -0.03333333334 Combine like terms: -1.000555401 + -0.03333333334 = -1.03388873434 x = -1.03388873434 Simplifying x = -1.03388873434Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.96722206766, -1.03388873434}
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