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Simplifying -0.1x2 + 0.6x + 7 = 0 Reorder the terms: 7 + 0.6x + -0.1x2 = 0 Solving 7 + 0.6x + -0.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. -70 + -6x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + -6x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + -6x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -6x + x2 = 0 + 70 -6x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 -6x + x2 = 70 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 70 + 9 Reorder the terms: 9 + -6x + x2 = 70 + 9 Combine like terms: 70 + 9 = 79 9 + -6x + x2 = 79 Factor a perfect square on the left side: (x + -3)(x + -3) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (x + -3) equal to 8.888194417 and -8.888194417.Subproblem 1
x + -3 = 8.888194417 Simplifying x + -3 = 8.888194417 Reorder the terms: -3 + x = 8.888194417 Solving -3 + x = 8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 8.888194417 + 3 Combine like terms: -3 + 3 = 0 0 + x = 8.888194417 + 3 x = 8.888194417 + 3 Combine like terms: 8.888194417 + 3 = 11.888194417 x = 11.888194417 Simplifying x = 11.888194417Subproblem 2
x + -3 = -8.888194417 Simplifying x + -3 = -8.888194417 Reorder the terms: -3 + x = -8.888194417 Solving -3 + x = -8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -8.888194417 + 3 Combine like terms: -3 + 3 = 0 0 + x = -8.888194417 + 3 x = -8.888194417 + 3 Combine like terms: -8.888194417 + 3 = -5.888194417 x = -5.888194417 Simplifying x = -5.888194417Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.888194417, -5.888194417}
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