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Simplifying 10x2 + 4x + -21 = 0 Reorder the terms: -21 + 4x + 10x2 = 0 Solving -21 + 4x + 10x2 = 0 Solving for variable 'x'. 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 Move the constant term to the right: Add '2.1' to each side of the equation. -2.1 + 0.4x + 2.1 + x2 = 0 + 2.1 Reorder the terms: -2.1 + 2.1 + 0.4x + x2 = 0 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + 0.4x + x2 = 0 + 2.1 0.4x + x2 = 0 + 2.1 Combine like terms: 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 = 1.262873884 x = 1.262873884 Simplifying x = 1.262873884Subproblem 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 = -1.662873884 x = -1.662873884 Simplifying x = -1.662873884Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.262873884, -1.662873884}
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