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Simplifying 1 + x = 3x * 5x Reorder the terms for easier multiplication: 1 + x = 3 * 5x * x Multiply 3 * 5 1 + x = 15x * x Multiply x * x 1 + x = 15x2 Solving 1 + x = 15x2 Solving for variable 'x'. Combine like terms: 15x2 + -15x2 = 0 1 + x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -0.06666666667 + -0.06666666667x + x2 = 0 Move the constant term to the right: Add '0.06666666667' to each side of the equation. -0.06666666667 + -0.06666666667x + 0.06666666667 + x2 = 0 + 0.06666666667 Reorder the terms: -0.06666666667 + 0.06666666667 + -0.06666666667x + x2 = 0 + 0.06666666667 Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000 0.00000000000 + -0.06666666667x + x2 = 0 + 0.06666666667 -0.06666666667x + x2 = 0 + 0.06666666667 Combine like terms: 0 + 0.06666666667 = 0.06666666667 -0.06666666667x + x2 = 0.06666666667 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.06666666667x + 0.25 + x2 = 0.06666666667 + 0.25 Reorder the terms: 0.25 + -0.06666666667x + x2 = 0.06666666667 + 0.25 Combine like terms: 0.06666666667 + 0.25 = 0.31666666667 0.25 + -0.06666666667x + x2 = 0.31666666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.31666666667 Calculate the square root of the right side: 0.562731434 Break this problem into two subproblems by setting (x + 0.5) equal to 0.562731434 and -0.562731434.Subproblem 1
x + 0.5 = 0.562731434 Simplifying x + 0.5 = 0.562731434 Reorder the terms: 0.5 + x = 0.562731434 Solving 0.5 + x = 0.562731434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.562731434 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.562731434 + -0.5 x = 0.562731434 + -0.5 Combine like terms: 0.562731434 + -0.5 = 0.062731434 x = 0.062731434 Simplifying x = 0.062731434Subproblem 2
x + 0.5 = -0.562731434 Simplifying x + 0.5 = -0.562731434 Reorder the terms: 0.5 + x = -0.562731434 Solving 0.5 + x = -0.562731434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.562731434 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.562731434 + -0.5 x = -0.562731434 + -0.5 Combine like terms: -0.562731434 + -0.5 = -1.062731434 x = -1.062731434 Simplifying x = -1.062731434Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.062731434, -1.062731434}
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