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Simplifying -0.1x2 + 0.6x + 7 = x Reorder the terms: 7 + 0.6x + -0.1x2 = x Solving 7 + 0.6x + -0.1x2 = x Solving for variable 'x'. Reorder the terms: 7 + 0.6x + -1x + -0.1x2 = x + -1x Combine like terms: 0.6x + -1x = -0.4x 7 + -0.4x + -0.1x2 = x + -1x Combine like terms: x + -1x = 0 7 + -0.4x + -0.1x2 = 0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -70 + 4x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + 4x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + 4x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 4x + x2 = 0 + 70 4x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 4x + x2 = 70 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 70 + 4 Reorder the terms: 4 + 4x + x2 = 70 + 4 Combine like terms: 70 + 4 = 74 4 + 4x + x2 = 74 Factor a perfect square on the left side: (x + 2)(x + 2) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (x + 2) equal to 8.602325267 and -8.602325267.Subproblem 1
x + 2 = 8.602325267 Simplifying x + 2 = 8.602325267 Reorder the terms: 2 + x = 8.602325267 Solving 2 + x = 8.602325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 8.602325267 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.602325267 + -2 x = 8.602325267 + -2 Combine like terms: 8.602325267 + -2 = 6.602325267 x = 6.602325267 Simplifying x = 6.602325267Subproblem 2
x + 2 = -8.602325267 Simplifying x + 2 = -8.602325267 Reorder the terms: 2 + x = -8.602325267 Solving 2 + x = -8.602325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -8.602325267 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.602325267 + -2 x = -8.602325267 + -2 Combine like terms: -8.602325267 + -2 = -10.602325267 x = -10.602325267 Simplifying x = -10.602325267Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.602325267, -10.602325267}
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