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Simplifying 5x2 + 10x = 12 Reorder the terms: 10x + 5x2 = 12 Solving 10x + 5x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 10x + 5x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + 2x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 2x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 2x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 2x + x2 = 0 + 2.4 2x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 2x + x2 = 2.4 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 2.4 + 1 Reorder the terms: 1 + 2x + x2 = 2.4 + 1 Combine like terms: 2.4 + 1 = 3.4 1 + 2x + x2 = 3.4 Factor a perfect square on the left side: (x + 1)(x + 1) = 3.4 Calculate the square root of the right side: 1.843908891 Break this problem into two subproblems by setting (x + 1) equal to 1.843908891 and -1.843908891.Subproblem 1
x + 1 = 1.843908891 Simplifying x + 1 = 1.843908891 Reorder the terms: 1 + x = 1.843908891 Solving 1 + x = 1.843908891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.843908891 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.843908891 + -1 x = 1.843908891 + -1 Combine like terms: 1.843908891 + -1 = 0.843908891 x = 0.843908891 Simplifying x = 0.843908891Subproblem 2
x + 1 = -1.843908891 Simplifying x + 1 = -1.843908891 Reorder the terms: 1 + x = -1.843908891 Solving 1 + x = -1.843908891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.843908891 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.843908891 + -1 x = -1.843908891 + -1 Combine like terms: -1.843908891 + -1 = -2.843908891 x = -2.843908891 Simplifying x = -2.843908891Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.843908891, -2.843908891}
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