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Simplifying 10x2 + 30x + 13 = 0 Reorder the terms: 13 + 30x + 10x2 = 0 Solving 13 + 30x + 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'. 1.3 + 3x + x2 = 0 Move the constant term to the right: Add '-1.3' to each side of the equation. 1.3 + 3x + -1.3 + x2 = 0 + -1.3 Reorder the terms: 1.3 + -1.3 + 3x + x2 = 0 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + 3x + x2 = 0 + -1.3 3x + x2 = 0 + -1.3 Combine like terms: 0 + -1.3 = -1.3 3x + x2 = -1.3 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -1.3 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -1.3 + 2.25 Combine like terms: -1.3 + 2.25 = 0.95 2.25 + 3x + x2 = 0.95 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 0.95 Calculate the square root of the right side: 0.974679434 Break this problem into two subproblems by setting (x + 1.5) equal to 0.974679434 and -0.974679434.Subproblem 1
x + 1.5 = 0.974679434 Simplifying x + 1.5 = 0.974679434 Reorder the terms: 1.5 + x = 0.974679434 Solving 1.5 + x = 0.974679434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 0.974679434 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 0.974679434 + -1.5 x = 0.974679434 + -1.5 Combine like terms: 0.974679434 + -1.5 = -0.525320566 x = -0.525320566 Simplifying x = -0.525320566Subproblem 2
x + 1.5 = -0.974679434 Simplifying x + 1.5 = -0.974679434 Reorder the terms: 1.5 + x = -0.974679434 Solving 1.5 + x = -0.974679434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -0.974679434 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -0.974679434 + -1.5 x = -0.974679434 + -1.5 Combine like terms: -0.974679434 + -1.5 = -2.474679434 x = -2.474679434 Simplifying x = -2.474679434Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.525320566, -2.474679434}
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