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Simplifying 0.4x2 + 3x + -70 = 0 Reorder the terms: -70 + 3x + 0.4x2 = 0 Solving -70 + 3x + 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'. -175 + 7.5x + x2 = 0 Move the constant term to the right: Add '175' to each side of the equation. -175 + 7.5x + 175 + x2 = 0 + 175 Reorder the terms: -175 + 175 + 7.5x + x2 = 0 + 175 Combine like terms: -175 + 175 = 0 0 + 7.5x + x2 = 0 + 175 7.5x + x2 = 0 + 175 Combine like terms: 0 + 175 = 175 7.5x + x2 = 175 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 175 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 175 + 14.0625 Combine like terms: 175 + 14.0625 = 189.0625 14.0625 + 7.5x + x2 = 189.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 189.0625 Calculate the square root of the right side: 13.75 Break this problem into two subproblems by setting (x + 3.75) equal to 13.75 and -13.75.Subproblem 1
x + 3.75 = 13.75 Simplifying x + 3.75 = 13.75 Reorder the terms: 3.75 + x = 13.75 Solving 3.75 + x = 13.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 13.75 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 13.75 + -3.75 x = 13.75 + -3.75 Combine like terms: 13.75 + -3.75 = 10 x = 10 Simplifying x = 10Subproblem 2
x + 3.75 = -13.75 Simplifying x + 3.75 = -13.75 Reorder the terms: 3.75 + x = -13.75 Solving 3.75 + x = -13.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -13.75 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -13.75 + -3.75 x = -13.75 + -3.75 Combine like terms: -13.75 + -3.75 = -17.5 x = -17.5 Simplifying x = -17.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {10, -17.5}
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