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Simplifying 16000000 = 0.7x2 + -4.3x + 5.5 Reorder the terms: 16000000 = 5.5 + -4.3x + 0.7x2 Solving 16000000 = 5.5 + -4.3x + 0.7x2 Solving for variable 'x'. Combine like terms: 16000000 + -5.5 = 15999994.5 15999994.5 + 4.3x + -0.7x2 = 5.5 + -4.3x + 0.7x2 + -5.5 + 4.3x + -0.7x2 Reorder the terms: 15999994.5 + 4.3x + -0.7x2 = 5.5 + -5.5 + -4.3x + 4.3x + 0.7x2 + -0.7x2 Combine like terms: 5.5 + -5.5 = 0.0 15999994.5 + 4.3x + -0.7x2 = 0.0 + -4.3x + 4.3x + 0.7x2 + -0.7x2 15999994.5 + 4.3x + -0.7x2 = -4.3x + 4.3x + 0.7x2 + -0.7x2 Combine like terms: -4.3x + 4.3x = 0.0 15999994.5 + 4.3x + -0.7x2 = 0.0 + 0.7x2 + -0.7x2 15999994.5 + 4.3x + -0.7x2 = 0.7x2 + -0.7x2 Combine like terms: 0.7x2 + -0.7x2 = 0.0 15999994.5 + 4.3x + -0.7x2 = 0.0 Begin completing the square. Divide all terms by -0.7 the coefficient of the squared term: Divide each side by '-0.7'. -22857135 + -6.142857143x + x2 = 0 Move the constant term to the right: Add '22857135' to each side of the equation. -22857135 + -6.142857143x + 22857135 + x2 = 0 + 22857135 Reorder the terms: -22857135 + 22857135 + -6.142857143x + x2 = 0 + 22857135 Combine like terms: -22857135 + 22857135 = 0 0 + -6.142857143x + x2 = 0 + 22857135 -6.142857143x + x2 = 0 + 22857135 Combine like terms: 0 + 22857135 = 22857135 -6.142857143x + x2 = 22857135 The x term is -6.142857143x. Take half its coefficient (-3.071428572). Square it (9.433673473) and add it to both sides. Add '9.433673473' to each side of the equation. -6.142857143x + 9.433673473 + x2 = 22857135 + 9.433673473 Reorder the terms: 9.433673473 + -6.142857143x + x2 = 22857135 + 9.433673473 Combine like terms: 22857135 + 9.433673473 = 22857144.433673473 9.433673473 + -6.142857143x + x2 = 22857144.433673473 Factor a perfect square on the left side: (x + -3.071428572)(x + -3.071428572) = 22857144.433673473 Calculate the square root of the right side: 4780.914602215 Break this problem into two subproblems by setting (x + -3.071428572) equal to 4780.914602215 and -4780.914602215.Subproblem 1
x + -3.071428572 = 4780.914602215 Simplifying x + -3.071428572 = 4780.914602215 Reorder the terms: -3.071428572 + x = 4780.914602215 Solving -3.071428572 + x = 4780.914602215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.071428572' to each side of the equation. -3.071428572 + 3.071428572 + x = 4780.914602215 + 3.071428572 Combine like terms: -3.071428572 + 3.071428572 = 0.000000000 0.000000000 + x = 4780.914602215 + 3.071428572 x = 4780.914602215 + 3.071428572 Combine like terms: 4780.914602215 + 3.071428572 = 4783.986030787 x = 4783.986030787 Simplifying x = 4783.986030787Subproblem 2
x + -3.071428572 = -4780.914602215 Simplifying x + -3.071428572 = -4780.914602215 Reorder the terms: -3.071428572 + x = -4780.914602215 Solving -3.071428572 + x = -4780.914602215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.071428572' to each side of the equation. -3.071428572 + 3.071428572 + x = -4780.914602215 + 3.071428572 Combine like terms: -3.071428572 + 3.071428572 = 0.000000000 0.000000000 + x = -4780.914602215 + 3.071428572 x = -4780.914602215 + 3.071428572 Combine like terms: -4780.914602215 + 3.071428572 = -4777.843173643 x = -4777.843173643 Simplifying x = -4777.843173643Solution
The solution to the problem is based on the solutions from the subproblems. x = {4783.986030787, -4777.843173643}
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