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Simplifying 15 = x + 5x2 Solving 15 = x + 5x2 Solving for variable 'x'. Reorder the terms: 15 + -1x + -5x2 = x + -1x + 5x2 + -5x2 Combine like terms: x + -1x = 0 15 + -1x + -5x2 = 0 + 5x2 + -5x2 15 + -1x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 15 + -1x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -3 + 0.2x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.2x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 0.2x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.2x + x2 = 0 + 3 0.2x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.2x + x2 = 3 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 3 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 3 + 0.01 Combine like terms: 3 + 0.01 = 3.01 0.01 + 0.2x + x2 = 3.01 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 3.01 Calculate the square root of the right side: 1.734935157 Break this problem into two subproblems by setting (x + 0.1) equal to 1.734935157 and -1.734935157.Subproblem 1
x + 0.1 = 1.734935157 Simplifying x + 0.1 = 1.734935157 Reorder the terms: 0.1 + x = 1.734935157 Solving 0.1 + x = 1.734935157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 1.734935157 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 1.734935157 + -0.1 x = 1.734935157 + -0.1 Combine like terms: 1.734935157 + -0.1 = 1.634935157 x = 1.634935157 Simplifying x = 1.634935157Subproblem 2
x + 0.1 = -1.734935157 Simplifying x + 0.1 = -1.734935157 Reorder the terms: 0.1 + x = -1.734935157 Solving 0.1 + x = -1.734935157 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -1.734935157 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -1.734935157 + -0.1 x = -1.734935157 + -0.1 Combine like terms: -1.734935157 + -0.1 = -1.834935157 x = -1.834935157 Simplifying x = -1.834935157Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.634935157, -1.834935157}
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