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Simplifying 0.4x2 + 0.6x + -7 = 0 Reorder the terms: -7 + 0.6x + 0.4x2 = 0 Solving -7 + 0.6x + 0.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. -17.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 1.5x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 1.5x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 1.5x + x2 = 0 + 17.5 1.5x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 1.5x + x2 = 17.5 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 17.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 17.5 + 0.5625 Combine like terms: 17.5 + 0.5625 = 18.0625 0.5625 + 1.5x + x2 = 18.0625 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 18.0625 Calculate the square root of the right side: 4.25 Break this problem into two subproblems by setting (x + 0.75) equal to 4.25 and -4.25.Subproblem 1
x + 0.75 = 4.25 Simplifying x + 0.75 = 4.25 Reorder the terms: 0.75 + x = 4.25 Solving 0.75 + x = 4.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 4.25 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 4.25 + -0.75 x = 4.25 + -0.75 Combine like terms: 4.25 + -0.75 = 3.5 x = 3.5 Simplifying x = 3.5Subproblem 2
x + 0.75 = -4.25 Simplifying x + 0.75 = -4.25 Reorder the terms: 0.75 + x = -4.25 Solving 0.75 + x = -4.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -4.25 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -4.25 + -0.75 x = -4.25 + -0.75 Combine like terms: -4.25 + -0.75 = -5 x = -5 Simplifying x = -5Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.5, -5}
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