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Simplifying 10.5 = 0.7x2 + -4.3x Reorder the terms: 10.5 = -4.3x + 0.7x2 Solving 10.5 = -4.3x + 0.7x2 Solving for variable 'x'. Reorder the terms: 10.5 + 4.3x + -0.7x2 = -4.3x + 4.3x + 0.7x2 + -0.7x2 Combine like terms: -4.3x + 4.3x = 0.0 10.5 + 4.3x + -0.7x2 = 0.0 + 0.7x2 + -0.7x2 10.5 + 4.3x + -0.7x2 = 0.7x2 + -0.7x2 Combine like terms: 0.7x2 + -0.7x2 = 0.0 10.5 + 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'. -15 + -6.142857143x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -6.142857143x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -6.142857143x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -6.142857143x + x2 = 0 + 15 -6.142857143x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -6.142857143x + x2 = 15 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 = 15 + 9.433673473 Reorder the terms: 9.433673473 + -6.142857143x + x2 = 15 + 9.433673473 Combine like terms: 15 + 9.433673473 = 24.433673473 9.433673473 + -6.142857143x + x2 = 24.433673473 Factor a perfect square on the left side: (x + -3.071428572)(x + -3.071428572) = 24.433673473 Calculate the square root of the right side: 4.943042937 Break this problem into two subproblems by setting (x + -3.071428572) equal to 4.943042937 and -4.943042937.Subproblem 1
x + -3.071428572 = 4.943042937 Simplifying x + -3.071428572 = 4.943042937 Reorder the terms: -3.071428572 + x = 4.943042937 Solving -3.071428572 + x = 4.943042937 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 = 4.943042937 + 3.071428572 Combine like terms: -3.071428572 + 3.071428572 = 0.000000000 0.000000000 + x = 4.943042937 + 3.071428572 x = 4.943042937 + 3.071428572 Combine like terms: 4.943042937 + 3.071428572 = 8.014471509 x = 8.014471509 Simplifying x = 8.014471509Subproblem 2
x + -3.071428572 = -4.943042937 Simplifying x + -3.071428572 = -4.943042937 Reorder the terms: -3.071428572 + x = -4.943042937 Solving -3.071428572 + x = -4.943042937 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 = -4.943042937 + 3.071428572 Combine like terms: -3.071428572 + 3.071428572 = 0.000000000 0.000000000 + x = -4.943042937 + 3.071428572 x = -4.943042937 + 3.071428572 Combine like terms: -4.943042937 + 3.071428572 = -1.871614365 x = -1.871614365 Simplifying x = -1.871614365Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.014471509, -1.871614365}
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