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Simplifying -73x2 + 13x + 20 = 0 Reorder the terms: 20 + 13x + -73x2 = 0 Solving 20 + 13x + -73x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -73 the coefficient of the squared term: Divide each side by '-73'. -0.2739726027 + -0.1780821918x + x2 = 0 Move the constant term to the right: Add '0.2739726027' to each side of the equation. -0.2739726027 + -0.1780821918x + 0.2739726027 + x2 = 0 + 0.2739726027 Reorder the terms: -0.2739726027 + 0.2739726027 + -0.1780821918x + x2 = 0 + 0.2739726027 Combine like terms: -0.2739726027 + 0.2739726027 = 0.0000000000 0.0000000000 + -0.1780821918x + x2 = 0 + 0.2739726027 -0.1780821918x + x2 = 0 + 0.2739726027 Combine like terms: 0 + 0.2739726027 = 0.2739726027 -0.1780821918x + x2 = 0.2739726027 The x term is -0.1780821918x. Take half its coefficient (-0.0890410959). Square it (0.007928316759) and add it to both sides. Add '0.007928316759' to each side of the equation. -0.1780821918x + 0.007928316759 + x2 = 0.2739726027 + 0.007928316759 Reorder the terms: 0.007928316759 + -0.1780821918x + x2 = 0.2739726027 + 0.007928316759 Combine like terms: 0.2739726027 + 0.007928316759 = 0.281900919459 0.007928316759 + -0.1780821918x + x2 = 0.281900919459 Factor a perfect square on the left side: (x + -0.0890410959)(x + -0.0890410959) = 0.281900919459 Calculate the square root of the right side: 0.530943424 Break this problem into two subproblems by setting (x + -0.0890410959) equal to 0.530943424 and -0.530943424.Subproblem 1
x + -0.0890410959 = 0.530943424 Simplifying x + -0.0890410959 = 0.530943424 Reorder the terms: -0.0890410959 + x = 0.530943424 Solving -0.0890410959 + x = 0.530943424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0890410959' to each side of the equation. -0.0890410959 + 0.0890410959 + x = 0.530943424 + 0.0890410959 Combine like terms: -0.0890410959 + 0.0890410959 = 0.0000000000 0.0000000000 + x = 0.530943424 + 0.0890410959 x = 0.530943424 + 0.0890410959 Combine like terms: 0.530943424 + 0.0890410959 = 0.6199845199 x = 0.6199845199 Simplifying x = 0.6199845199Subproblem 2
x + -0.0890410959 = -0.530943424 Simplifying x + -0.0890410959 = -0.530943424 Reorder the terms: -0.0890410959 + x = -0.530943424 Solving -0.0890410959 + x = -0.530943424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0890410959' to each side of the equation. -0.0890410959 + 0.0890410959 + x = -0.530943424 + 0.0890410959 Combine like terms: -0.0890410959 + 0.0890410959 = 0.0000000000 0.0000000000 + x = -0.530943424 + 0.0890410959 x = -0.530943424 + 0.0890410959 Combine like terms: -0.530943424 + 0.0890410959 = -0.4419023281 x = -0.4419023281 Simplifying x = -0.4419023281Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6199845199, -0.4419023281}
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