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Simplifying -5x2 + 72x + 378 = 0 Reorder the terms: 378 + 72x + -5x2 = 0 Solving 378 + 72x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -75.6 + -14.4x + x2 = 0 Move the constant term to the right: Add '75.6' to each side of the equation. -75.6 + -14.4x + 75.6 + x2 = 0 + 75.6 Reorder the terms: -75.6 + 75.6 + -14.4x + x2 = 0 + 75.6 Combine like terms: -75.6 + 75.6 = 0.0 0.0 + -14.4x + x2 = 0 + 75.6 -14.4x + x2 = 0 + 75.6 Combine like terms: 0 + 75.6 = 75.6 -14.4x + x2 = 75.6 The x term is -14.4x. Take half its coefficient (-7.2). Square it (51.84) and add it to both sides. Add '51.84' to each side of the equation. -14.4x + 51.84 + x2 = 75.6 + 51.84 Reorder the terms: 51.84 + -14.4x + x2 = 75.6 + 51.84 Combine like terms: 75.6 + 51.84 = 127.44 51.84 + -14.4x + x2 = 127.44 Factor a perfect square on the left side: (x + -7.2)(x + -7.2) = 127.44 Calculate the square root of the right side: 11.288932633 Break this problem into two subproblems by setting (x + -7.2) equal to 11.288932633 and -11.288932633.Subproblem 1
x + -7.2 = 11.288932633 Simplifying x + -7.2 = 11.288932633 Reorder the terms: -7.2 + x = 11.288932633 Solving -7.2 + x = 11.288932633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.2' to each side of the equation. -7.2 + 7.2 + x = 11.288932633 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + x = 11.288932633 + 7.2 x = 11.288932633 + 7.2 Combine like terms: 11.288932633 + 7.2 = 18.488932633 x = 18.488932633 Simplifying x = 18.488932633Subproblem 2
x + -7.2 = -11.288932633 Simplifying x + -7.2 = -11.288932633 Reorder the terms: -7.2 + x = -11.288932633 Solving -7.2 + x = -11.288932633 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.2' to each side of the equation. -7.2 + 7.2 + x = -11.288932633 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + x = -11.288932633 + 7.2 x = -11.288932633 + 7.2 Combine like terms: -11.288932633 + 7.2 = -4.088932633 x = -4.088932633 Simplifying x = -4.088932633Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.488932633, -4.088932633}
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