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Simplifying 10x(2x + 1) + -6x = 13 Reorder the terms: 10x(1 + 2x) + -6x = 13 (1 * 10x + 2x * 10x) + -6x = 13 (10x + 20x2) + -6x = 13 Reorder the terms: 10x + -6x + 20x2 = 13 Combine like terms: 10x + -6x = 4x 4x + 20x2 = 13 Solving 4x + 20x2 = 13 Solving for variable 'x'. Reorder the terms: -13 + 4x + 20x2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + 4x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.65 + 0.2x + x2 = 0.0 Move the constant term to the right: Add '0.65' to each side of the equation. -0.65 + 0.2x + 0.65 + x2 = 0.0 + 0.65 Reorder the terms: -0.65 + 0.65 + 0.2x + x2 = 0.0 + 0.65 Combine like terms: -0.65 + 0.65 = 0.00 0.00 + 0.2x + x2 = 0.0 + 0.65 0.2x + x2 = 0.0 + 0.65 Combine like terms: 0.0 + 0.65 = 0.65 0.2x + x2 = 0.65 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 0.65 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.65 + 0.01 Combine like terms: 0.65 + 0.01 = 0.66 0.01 + 0.2x + x2 = 0.66 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.66 Calculate the square root of the right side: 0.81240384 Break this problem into two subproblems by setting (x + 0.1) equal to 0.81240384 and -0.81240384.Subproblem 1
x + 0.1 = 0.81240384 Simplifying x + 0.1 = 0.81240384 Reorder the terms: 0.1 + x = 0.81240384 Solving 0.1 + x = 0.81240384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 0.81240384 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.81240384 + -0.1 x = 0.81240384 + -0.1 Combine like terms: 0.81240384 + -0.1 = 0.71240384 x = 0.71240384 Simplifying x = 0.71240384Subproblem 2
x + 0.1 = -0.81240384 Simplifying x + 0.1 = -0.81240384 Reorder the terms: 0.1 + x = -0.81240384 Solving 0.1 + x = -0.81240384 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -0.81240384 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.81240384 + -0.1 x = -0.81240384 + -0.1 Combine like terms: -0.81240384 + -0.1 = -0.91240384 x = -0.91240384 Simplifying x = -0.91240384Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.71240384, -0.91240384}
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