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Simplifying 72x(3x + -78) + 42x(x) = 721 Reorder the terms: 72x(-78 + 3x) + 42x(x) = 721 (-78 * 72x + 3x * 72x) + 42x(x) = 721 (-5616x + 216x2) + 42x(x) = 721 Multiply x * x -5616x + 216x2 + 42x2 = 721 Combine like terms: 216x2 + 42x2 = 258x2 -5616x + 258x2 = 721 Solving -5616x + 258x2 = 721 Solving for variable 'x'. Reorder the terms: -721 + -5616x + 258x2 = 721 + -721 Combine like terms: 721 + -721 = 0 -721 + -5616x + 258x2 = 0 Begin completing the square. Divide all terms by 258 the coefficient of the squared term: Divide each side by '258'. -2.794573643 + -21.76744186x + x2 = 0 Move the constant term to the right: Add '2.794573643' to each side of the equation. -2.794573643 + -21.76744186x + 2.794573643 + x2 = 0 + 2.794573643 Reorder the terms: -2.794573643 + 2.794573643 + -21.76744186x + x2 = 0 + 2.794573643 Combine like terms: -2.794573643 + 2.794573643 = 0.000000000 0.000000000 + -21.76744186x + x2 = 0 + 2.794573643 -21.76744186x + x2 = 0 + 2.794573643 Combine like terms: 0 + 2.794573643 = 2.794573643 -21.76744186x + x2 = 2.794573643 The x term is -21.76744186x. Take half its coefficient (-10.88372093). Square it (118.4553813) and add it to both sides. Add '118.4553813' to each side of the equation. -21.76744186x + 118.4553813 + x2 = 2.794573643 + 118.4553813 Reorder the terms: 118.4553813 + -21.76744186x + x2 = 2.794573643 + 118.4553813 Combine like terms: 2.794573643 + 118.4553813 = 121.249954943 118.4553813 + -21.76744186x + x2 = 121.249954943 Factor a perfect square on the left side: (x + -10.88372093)(x + -10.88372093) = 121.249954943 Calculate the square root of the right side: 11.011355727 Break this problem into two subproblems by setting (x + -10.88372093) equal to 11.011355727 and -11.011355727.Subproblem 1
x + -10.88372093 = 11.011355727 Simplifying x + -10.88372093 = 11.011355727 Reorder the terms: -10.88372093 + x = 11.011355727 Solving -10.88372093 + x = 11.011355727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.88372093' to each side of the equation. -10.88372093 + 10.88372093 + x = 11.011355727 + 10.88372093 Combine like terms: -10.88372093 + 10.88372093 = 0.00000000 0.00000000 + x = 11.011355727 + 10.88372093 x = 11.011355727 + 10.88372093 Combine like terms: 11.011355727 + 10.88372093 = 21.895076657 x = 21.895076657 Simplifying x = 21.895076657Subproblem 2
x + -10.88372093 = -11.011355727 Simplifying x + -10.88372093 = -11.011355727 Reorder the terms: -10.88372093 + x = -11.011355727 Solving -10.88372093 + x = -11.011355727 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.88372093' to each side of the equation. -10.88372093 + 10.88372093 + x = -11.011355727 + 10.88372093 Combine like terms: -10.88372093 + 10.88372093 = 0.00000000 0.00000000 + x = -11.011355727 + 10.88372093 x = -11.011355727 + 10.88372093 Combine like terms: -11.011355727 + 10.88372093 = -0.127634797 x = -0.127634797 Simplifying x = -0.127634797Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.895076657, -0.127634797}
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