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Simplifying -15 + 33x + 10x2 = 0 Solving -15 + 33x + 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'. -1.5 + 3.3x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + 3.3x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + 3.3x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + 3.3x + x2 = 0 + 1.5 3.3x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 3.3x + x2 = 1.5 The x term is 3.3x. Take half its coefficient (1.65). Square it (2.7225) and add it to both sides. Add '2.7225' to each side of the equation. 3.3x + 2.7225 + x2 = 1.5 + 2.7225 Reorder the terms: 2.7225 + 3.3x + x2 = 1.5 + 2.7225 Combine like terms: 1.5 + 2.7225 = 4.2225 2.7225 + 3.3x + x2 = 4.2225 Factor a perfect square on the left side: (x + 1.65)(x + 1.65) = 4.2225 Calculate the square root of the right side: 2.054872259 Break this problem into two subproblems by setting (x + 1.65) equal to 2.054872259 and -2.054872259.Subproblem 1
x + 1.65 = 2.054872259 Simplifying x + 1.65 = 2.054872259 Reorder the terms: 1.65 + x = 2.054872259 Solving 1.65 + x = 2.054872259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.65' to each side of the equation. 1.65 + -1.65 + x = 2.054872259 + -1.65 Combine like terms: 1.65 + -1.65 = 0.00 0.00 + x = 2.054872259 + -1.65 x = 2.054872259 + -1.65 Combine like terms: 2.054872259 + -1.65 = 0.404872259 x = 0.404872259 Simplifying x = 0.404872259Subproblem 2
x + 1.65 = -2.054872259 Simplifying x + 1.65 = -2.054872259 Reorder the terms: 1.65 + x = -2.054872259 Solving 1.65 + x = -2.054872259 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.65' to each side of the equation. 1.65 + -1.65 + x = -2.054872259 + -1.65 Combine like terms: 1.65 + -1.65 = 0.00 0.00 + x = -2.054872259 + -1.65 x = -2.054872259 + -1.65 Combine like terms: -2.054872259 + -1.65 = -3.704872259 x = -3.704872259 Simplifying x = -3.704872259Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.404872259, -3.704872259}
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