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Simplifying 2x(5x + -2) = 21 Reorder the terms: 2x(-2 + 5x) = 21 (-2 * 2x + 5x * 2x) = 21 (-4x + 10x2) = 21 Solving -4x + 10x2 = 21 Solving for variable 'x'. Reorder the terms: -21 + -4x + 10x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + -4x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.1 + -0.4x + x2 = 0.0 Move the constant term to the right: Add '2.1' to each side of the equation. -2.1 + -0.4x + 2.1 + x2 = 0.0 + 2.1 Reorder the terms: -2.1 + 2.1 + -0.4x + x2 = 0.0 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + -0.4x + x2 = 0.0 + 2.1 -0.4x + x2 = 0.0 + 2.1 Combine like terms: 0.0 + 2.1 = 2.1 -0.4x + x2 = 2.1 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 = 2.1 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 2.1 + 0.04 Combine like terms: 2.1 + 0.04 = 2.14 0.04 + -0.4x + x2 = 2.14 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 2.14 Calculate the square root of the right side: 1.462873884 Break this problem into two subproblems by setting (x + -0.2) equal to 1.462873884 and -1.462873884.Subproblem 1
x + -0.2 = 1.462873884 Simplifying x + -0.2 = 1.462873884 Reorder the terms: -0.2 + x = 1.462873884 Solving -0.2 + x = 1.462873884 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 = 1.462873884 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.462873884 + 0.2 x = 1.462873884 + 0.2 Combine like terms: 1.462873884 + 0.2 = 1.662873884 x = 1.662873884 Simplifying x = 1.662873884Subproblem 2
x + -0.2 = -1.462873884 Simplifying x + -0.2 = -1.462873884 Reorder the terms: -0.2 + x = -1.462873884 Solving -0.2 + x = -1.462873884 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 = -1.462873884 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.462873884 + 0.2 x = -1.462873884 + 0.2 Combine like terms: -1.462873884 + 0.2 = -1.262873884 x = -1.262873884 Simplifying x = -1.262873884Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.662873884, -1.262873884}
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