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Simplifying 4x2 + -15x + 7 = 0 Reorder the terms: 7 + -15x + 4x2 = 0 Solving 7 + -15x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.75 + -3.75x + x2 = 0 Move the constant term to the right: Add '-1.75' to each side of the equation. 1.75 + -3.75x + -1.75 + x2 = 0 + -1.75 Reorder the terms: 1.75 + -1.75 + -3.75x + x2 = 0 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + -3.75x + x2 = 0 + -1.75 -3.75x + x2 = 0 + -1.75 Combine like terms: 0 + -1.75 = -1.75 -3.75x + x2 = -1.75 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = -1.75 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = -1.75 + 3.515625 Combine like terms: -1.75 + 3.515625 = 1.765625 3.515625 + -3.75x + x2 = 1.765625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 1.765625 Calculate the square root of the right side: 1.328768227 Break this problem into two subproblems by setting (x + -1.875) equal to 1.328768227 and -1.328768227.Subproblem 1
x + -1.875 = 1.328768227 Simplifying x + -1.875 = 1.328768227 Reorder the terms: -1.875 + x = 1.328768227 Solving -1.875 + x = 1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 1.328768227 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 1.328768227 + 1.875 x = 1.328768227 + 1.875 Combine like terms: 1.328768227 + 1.875 = 3.203768227 x = 3.203768227 Simplifying x = 3.203768227Subproblem 2
x + -1.875 = -1.328768227 Simplifying x + -1.875 = -1.328768227 Reorder the terms: -1.875 + x = -1.328768227 Solving -1.875 + x = -1.328768227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -1.328768227 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -1.328768227 + 1.875 x = -1.328768227 + 1.875 Combine like terms: -1.328768227 + 1.875 = 0.546231773 x = 0.546231773 Simplifying x = 0.546231773Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.203768227, 0.546231773}
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