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Simplifying 5x2 = 2x + 18 Reorder the terms: 5x2 = 18 + 2x Solving 5x2 = 18 + 2x Solving for variable 'x'. Reorder the terms: -18 + -2x + 5x2 = 18 + 2x + -18 + -2x Reorder the terms: -18 + -2x + 5x2 = 18 + -18 + 2x + -2x Combine like terms: 18 + -18 = 0 -18 + -2x + 5x2 = 0 + 2x + -2x -18 + -2x + 5x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -18 + -2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.6 + -0.4x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + -0.4x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + -0.4x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + -0.4x + x2 = 0 + 3.6 -0.4x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 -0.4x + x2 = 3.6 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 3.6 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 3.6 + 0.04 Combine like terms: 3.6 + 0.04 = 3.64 0.04 + -0.4x + x2 = 3.64 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 3.64 Calculate the square root of the right side: 1.907878403 Break this problem into two subproblems by setting (x + -0.2) equal to 1.907878403 and -1.907878403.Subproblem 1
x + -0.2 = 1.907878403 Simplifying x + -0.2 = 1.907878403 Reorder the terms: -0.2 + x = 1.907878403 Solving -0.2 + x = 1.907878403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 1.907878403 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.907878403 + 0.2 x = 1.907878403 + 0.2 Combine like terms: 1.907878403 + 0.2 = 2.107878403 x = 2.107878403 Simplifying x = 2.107878403Subproblem 2
x + -0.2 = -1.907878403 Simplifying x + -0.2 = -1.907878403 Reorder the terms: -0.2 + x = -1.907878403 Solving -0.2 + x = -1.907878403 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -1.907878403 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.907878403 + 0.2 x = -1.907878403 + 0.2 Combine like terms: -1.907878403 + 0.2 = -1.707878403 x = -1.707878403 Simplifying x = -1.707878403Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.107878403, -1.707878403}
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