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Simplifying 5x2 + -18x + 7 = 0 Reorder the terms: 7 + -18x + 5x2 = 0 Solving 7 + -18x + 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'. 1.4 + -3.6x + x2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -3.6x + -1.4 + x2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -3.6x + x2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -3.6x + x2 = 0 + -1.4 -3.6x + x2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -3.6x + x2 = -1.4 The x term is -3.6x. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x + 3.24 + x2 = -1.4 + 3.24 Reorder the terms: 3.24 + -3.6x + x2 = -1.4 + 3.24 Combine like terms: -1.4 + 3.24 = 1.84 3.24 + -3.6x + x2 = 1.84 Factor a perfect square on the left side: (x + -1.8)(x + -1.8) = 1.84 Calculate the square root of the right side: 1.356465997 Break this problem into two subproblems by setting (x + -1.8) equal to 1.356465997 and -1.356465997.Subproblem 1
x + -1.8 = 1.356465997 Simplifying x + -1.8 = 1.356465997 Reorder the terms: -1.8 + x = 1.356465997 Solving -1.8 + x = 1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 1.356465997 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 1.356465997 + 1.8 x = 1.356465997 + 1.8 Combine like terms: 1.356465997 + 1.8 = 3.156465997 x = 3.156465997 Simplifying x = 3.156465997Subproblem 2
x + -1.8 = -1.356465997 Simplifying x + -1.8 = -1.356465997 Reorder the terms: -1.8 + x = -1.356465997 Solving -1.8 + x = -1.356465997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -1.356465997 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -1.356465997 + 1.8 x = -1.356465997 + 1.8 Combine like terms: -1.356465997 + 1.8 = 0.443534003 x = 0.443534003 Simplifying x = 0.443534003Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.156465997, 0.443534003}
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