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Simplifying 7.2(0.12 + -0.70x + x2) = x (0.12 * 7.2 + -0.70x * 7.2 + x2 * 7.2) = x (0.864 + -5.04x + 7.2x2) = x Solving 0.864 + -5.04x + 7.2x2 = x Solving for variable 'x'. Reorder the terms: 0.864 + -5.04x + -1x + 7.2x2 = x + -1x Combine like terms: -5.04x + -1x = -6.04x 0.864 + -6.04x + 7.2x2 = x + -1x Combine like terms: x + -1x = 0 0.864 + -6.04x + 7.2x2 = 0 Begin completing the square. Divide all terms by 7.2 the coefficient of the squared term: Divide each side by '7.2'. 0.12 + -0.8388888889x + x2 = 0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + -0.8388888889x + -0.12 + x2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + -0.8388888889x + x2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + -0.8388888889x + x2 = 0 + -0.12 -0.8388888889x + x2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 -0.8388888889x + x2 = -0.12 The x term is -0.8388888889x. Take half its coefficient (-0.4194444445). Square it (0.1759336420) and add it to both sides. Add '0.1759336420' to each side of the equation. -0.8388888889x + 0.1759336420 + x2 = -0.12 + 0.1759336420 Reorder the terms: 0.1759336420 + -0.8388888889x + x2 = -0.12 + 0.1759336420 Combine like terms: -0.12 + 0.1759336420 = 0.055933642 0.1759336420 + -0.8388888889x + x2 = 0.055933642 Factor a perfect square on the left side: (x + -0.4194444445)(x + -0.4194444445) = 0.055933642 Calculate the square root of the right side: 0.236502943 Break this problem into two subproblems by setting (x + -0.4194444445) equal to 0.236502943 and -0.236502943.Subproblem 1
x + -0.4194444445 = 0.236502943 Simplifying x + -0.4194444445 = 0.236502943 Reorder the terms: -0.4194444445 + x = 0.236502943 Solving -0.4194444445 + x = 0.236502943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4194444445' to each side of the equation. -0.4194444445 + 0.4194444445 + x = 0.236502943 + 0.4194444445 Combine like terms: -0.4194444445 + 0.4194444445 = 0.0000000000 0.0000000000 + x = 0.236502943 + 0.4194444445 x = 0.236502943 + 0.4194444445 Combine like terms: 0.236502943 + 0.4194444445 = 0.6559473875 x = 0.6559473875 Simplifying x = 0.6559473875Subproblem 2
x + -0.4194444445 = -0.236502943 Simplifying x + -0.4194444445 = -0.236502943 Reorder the terms: -0.4194444445 + x = -0.236502943 Solving -0.4194444445 + x = -0.236502943 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4194444445' to each side of the equation. -0.4194444445 + 0.4194444445 + x = -0.236502943 + 0.4194444445 Combine like terms: -0.4194444445 + 0.4194444445 = 0.0000000000 0.0000000000 + x = -0.236502943 + 0.4194444445 x = -0.236502943 + 0.4194444445 Combine like terms: -0.236502943 + 0.4194444445 = 0.1829415015 x = 0.1829415015 Simplifying x = 0.1829415015Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6559473875, 0.1829415015}
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