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Simplifying 10x2 + 26x + -3 = 0 Reorder the terms: -3 + 26x + 10x2 = 0 Solving -3 + 26x + 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'. -0.3 + 2.6x + x2 = 0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 2.6x + 0.3 + x2 = 0 + 0.3 Reorder the terms: -0.3 + 0.3 + 2.6x + x2 = 0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 2.6x + x2 = 0 + 0.3 2.6x + x2 = 0 + 0.3 Combine like terms: 0 + 0.3 = 0.3 2.6x + x2 = 0.3 The x term is 2.6x. Take half its coefficient (1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. 2.6x + 1.69 + x2 = 0.3 + 1.69 Reorder the terms: 1.69 + 2.6x + x2 = 0.3 + 1.69 Combine like terms: 0.3 + 1.69 = 1.99 1.69 + 2.6x + x2 = 1.99 Factor a perfect square on the left side: (x + 1.3)(x + 1.3) = 1.99 Calculate the square root of the right side: 1.410673598 Break this problem into two subproblems by setting (x + 1.3) equal to 1.410673598 and -1.410673598.Subproblem 1
x + 1.3 = 1.410673598 Simplifying x + 1.3 = 1.410673598 Reorder the terms: 1.3 + x = 1.410673598 Solving 1.3 + x = 1.410673598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = 1.410673598 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = 1.410673598 + -1.3 x = 1.410673598 + -1.3 Combine like terms: 1.410673598 + -1.3 = 0.110673598 x = 0.110673598 Simplifying x = 0.110673598Subproblem 2
x + 1.3 = -1.410673598 Simplifying x + 1.3 = -1.410673598 Reorder the terms: 1.3 + x = -1.410673598 Solving 1.3 + x = -1.410673598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3' to each side of the equation. 1.3 + -1.3 + x = -1.410673598 + -1.3 Combine like terms: 1.3 + -1.3 = 0.0 0.0 + x = -1.410673598 + -1.3 x = -1.410673598 + -1.3 Combine like terms: -1.410673598 + -1.3 = -2.710673598 x = -2.710673598 Simplifying x = -2.710673598Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.110673598, -2.710673598}
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