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Simplifying 0.6 = -5x2 + 7x Reorder the terms: 0.6 = 7x + -5x2 Solving 0.6 = 7x + -5x2 Solving for variable 'x'. Reorder the terms: 0.6 + -7x + 5x2 = 7x + -7x + -5x2 + 5x2 Combine like terms: 7x + -7x = 0 0.6 + -7x + 5x2 = 0 + -5x2 + 5x2 0.6 + -7x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 0.6 + -7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.12 + -1.4x + x2 = 0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + -1.4x + -0.12 + x2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + -1.4x + x2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + -1.4x + x2 = 0 + -0.12 -1.4x + x2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 -1.4x + x2 = -0.12 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = -0.12 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = -0.12 + 0.49 Combine like terms: -0.12 + 0.49 = 0.37 0.49 + -1.4x + x2 = 0.37 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 0.37 Calculate the square root of the right side: 0.608276253 Break this problem into two subproblems by setting (x + -0.7) equal to 0.608276253 and -0.608276253.Subproblem 1
x + -0.7 = 0.608276253 Simplifying x + -0.7 = 0.608276253 Reorder the terms: -0.7 + x = 0.608276253 Solving -0.7 + x = 0.608276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 0.608276253 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 0.608276253 + 0.7 x = 0.608276253 + 0.7 Combine like terms: 0.608276253 + 0.7 = 1.308276253 x = 1.308276253 Simplifying x = 1.308276253Subproblem 2
x + -0.7 = -0.608276253 Simplifying x + -0.7 = -0.608276253 Reorder the terms: -0.7 + x = -0.608276253 Solving -0.7 + x = -0.608276253 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -0.608276253 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -0.608276253 + 0.7 x = -0.608276253 + 0.7 Combine like terms: -0.608276253 + 0.7 = 0.091723747 x = 0.091723747 Simplifying x = 0.091723747Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.308276253, 0.091723747}
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