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Simplifying 0 = 4x2 + -45x + 40 Reorder the terms: 0 = 40 + -45x + 4x2 Solving 0 = 40 + -45x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -40 = -40 -40 + 45x + -4x2 = 40 + -45x + 4x2 + -40 + 45x + -4x2 Reorder the terms: -40 + 45x + -4x2 = 40 + -40 + -45x + 45x + 4x2 + -4x2 Combine like terms: 40 + -40 = 0 -40 + 45x + -4x2 = 0 + -45x + 45x + 4x2 + -4x2 -40 + 45x + -4x2 = -45x + 45x + 4x2 + -4x2 Combine like terms: -45x + 45x = 0 -40 + 45x + -4x2 = 0 + 4x2 + -4x2 -40 + 45x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -40 + 45x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 10 + -11.25x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -11.25x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -11.25x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -11.25x + x2 = 0 + -10 -11.25x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -11.25x + x2 = -10 The x term is -11.25x. Take half its coefficient (-5.625). Square it (31.640625) and add it to both sides. Add '31.640625' to each side of the equation. -11.25x + 31.640625 + x2 = -10 + 31.640625 Reorder the terms: 31.640625 + -11.25x + x2 = -10 + 31.640625 Combine like terms: -10 + 31.640625 = 21.640625 31.640625 + -11.25x + x2 = 21.640625 Factor a perfect square on the left side: (x + -5.625)(x + -5.625) = 21.640625 Calculate the square root of the right side: 4.651948516 Break this problem into two subproblems by setting (x + -5.625) equal to 4.651948516 and -4.651948516.Subproblem 1
x + -5.625 = 4.651948516 Simplifying x + -5.625 = 4.651948516 Reorder the terms: -5.625 + x = 4.651948516 Solving -5.625 + x = 4.651948516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = 4.651948516 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = 4.651948516 + 5.625 x = 4.651948516 + 5.625 Combine like terms: 4.651948516 + 5.625 = 10.276948516 x = 10.276948516 Simplifying x = 10.276948516Subproblem 2
x + -5.625 = -4.651948516 Simplifying x + -5.625 = -4.651948516 Reorder the terms: -5.625 + x = -4.651948516 Solving -5.625 + x = -4.651948516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.625' to each side of the equation. -5.625 + 5.625 + x = -4.651948516 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + x = -4.651948516 + 5.625 x = -4.651948516 + 5.625 Combine like terms: -4.651948516 + 5.625 = 0.973051484 x = 0.973051484 Simplifying x = 0.973051484Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.276948516, 0.973051484}
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