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Simplifying (5x2 + 6x + 2) + -1(5x + 3) = 0 Reorder the terms: (2 + 6x + 5x2) + -1(5x + 3) = 0 Remove parenthesis around (2 + 6x + 5x2) 2 + 6x + 5x2 + -1(5x + 3) = 0 Reorder the terms: 2 + 6x + 5x2 + -1(3 + 5x) = 0 2 + 6x + 5x2 + (3 * -1 + 5x * -1) = 0 2 + 6x + 5x2 + (-3 + -5x) = 0 Reorder the terms: 2 + -3 + 6x + -5x + 5x2 = 0 Combine like terms: 2 + -3 = -1 -1 + 6x + -5x + 5x2 = 0 Combine like terms: 6x + -5x = 1x -1 + 1x + 5x2 = 0 Solving -1 + 1x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + 0.2x + x2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 0.2x + 0.2 + x2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 0.2x + x2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 0.2x + x2 = 0 + 0.2 0.2x + x2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 0.2x + x2 = 0.2 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 = 0.2 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.2 + 0.01 Combine like terms: 0.2 + 0.01 = 0.21 0.01 + 0.2x + x2 = 0.21 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.21 Calculate the square root of the right side: 0.458257569 Break this problem into two subproblems by setting (x + 0.1) equal to 0.458257569 and -0.458257569.Subproblem 1
x + 0.1 = 0.458257569 Simplifying x + 0.1 = 0.458257569 Reorder the terms: 0.1 + x = 0.458257569 Solving 0.1 + x = 0.458257569 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 = 0.458257569 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.458257569 + -0.1 x = 0.458257569 + -0.1 Combine like terms: 0.458257569 + -0.1 = 0.358257569 x = 0.358257569 Simplifying x = 0.358257569Subproblem 2
x + 0.1 = -0.458257569 Simplifying x + 0.1 = -0.458257569 Reorder the terms: 0.1 + x = -0.458257569 Solving 0.1 + x = -0.458257569 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 = -0.458257569 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.458257569 + -0.1 x = -0.458257569 + -0.1 Combine like terms: -0.458257569 + -0.1 = -0.558257569 x = -0.558257569 Simplifying x = -0.558257569Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.358257569, -0.558257569}
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