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Simplifying 15x + -4 = x2 Reorder the terms: -4 + 15x = x2 Solving -4 + 15x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 -4 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -15x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -15x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -15x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -15x + x2 = 0 + -4 -15x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -15x + x2 = -4 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -4 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -4 + 56.25 Combine like terms: -4 + 56.25 = 52.25 56.25 + -15x + x2 = 52.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x + -7.5) equal to 7.228416147 and -7.228416147.Subproblem 1
x + -7.5 = 7.228416147 Simplifying x + -7.5 = 7.228416147 Reorder the terms: -7.5 + x = 7.228416147 Solving -7.5 + x = 7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 7.228416147 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.228416147 + 7.5 x = 7.228416147 + 7.5 Combine like terms: 7.228416147 + 7.5 = 14.728416147 x = 14.728416147 Simplifying x = 14.728416147Subproblem 2
x + -7.5 = -7.228416147 Simplifying x + -7.5 = -7.228416147 Reorder the terms: -7.5 + x = -7.228416147 Solving -7.5 + x = -7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -7.228416147 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.228416147 + 7.5 x = -7.228416147 + 7.5 Combine like terms: -7.228416147 + 7.5 = 0.271583853 x = 0.271583853 Simplifying x = 0.271583853Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.728416147, 0.271583853}
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