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Simplifying 5x2 = -1(10x + 2) Reorder the terms: 5x2 = -1(2 + 10x) 5x2 = (2 * -1 + 10x * -1) 5x2 = (-2 + -10x) Solving 5x2 = -2 + -10x Solving for variable 'x'. Reorder the terms: 2 + 10x + 5x2 = -2 + -10x + 2 + 10x Reorder the terms: 2 + 10x + 5x2 = -2 + 2 + -10x + 10x Combine like terms: -2 + 2 = 0 2 + 10x + 5x2 = 0 + -10x + 10x 2 + 10x + 5x2 = -10x + 10x Combine like terms: -10x + 10x = 0 2 + 10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 2x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 2x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 2x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 2x + x2 = 0 + -0.4 2x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 2x + x2 = -0.4 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 = -0.4 + 1 Reorder the terms: 1 + 2x + x2 = -0.4 + 1 Combine like terms: -0.4 + 1 = 0.6 1 + 2x + x2 = 0.6 Factor a perfect square on the left side: (x + 1)(x + 1) = 0.6 Calculate the square root of the right side: 0.774596669 Break this problem into two subproblems by setting (x + 1) equal to 0.774596669 and -0.774596669.Subproblem 1
x + 1 = 0.774596669 Simplifying x + 1 = 0.774596669 Reorder the terms: 1 + x = 0.774596669 Solving 1 + x = 0.774596669 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 = 0.774596669 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0.774596669 + -1 x = 0.774596669 + -1 Combine like terms: 0.774596669 + -1 = -0.225403331 x = -0.225403331 Simplifying x = -0.225403331Subproblem 2
x + 1 = -0.774596669 Simplifying x + 1 = -0.774596669 Reorder the terms: 1 + x = -0.774596669 Solving 1 + x = -0.774596669 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 = -0.774596669 + -1 Combine like terms: 1 + -1 = 0 0 + x = -0.774596669 + -1 x = -0.774596669 + -1 Combine like terms: -0.774596669 + -1 = -1.774596669 x = -1.774596669 Simplifying x = -1.774596669Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.225403331, -1.774596669}
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