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Simplifying 0.3 = x2 + -14x + 33 Reorder the terms: 0.3 = 33 + -14x + x2 Solving 0.3 = 33 + -14x + x2 Solving for variable 'x'. Combine like terms: 0.3 + -33 = -32.7 -32.7 + 14x + -1x2 = 33 + -14x + x2 + -33 + 14x + -1x2 Reorder the terms: -32.7 + 14x + -1x2 = 33 + -33 + -14x + 14x + x2 + -1x2 Combine like terms: 33 + -33 = 0 -32.7 + 14x + -1x2 = 0 + -14x + 14x + x2 + -1x2 -32.7 + 14x + -1x2 = -14x + 14x + x2 + -1x2 Combine like terms: -14x + 14x = 0 -32.7 + 14x + -1x2 = 0 + x2 + -1x2 -32.7 + 14x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -32.7 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 32.7 + -14x + x2 = 0 Move the constant term to the right: Add '-32.7' to each side of the equation. 32.7 + -14x + -32.7 + x2 = 0 + -32.7 Reorder the terms: 32.7 + -32.7 + -14x + x2 = 0 + -32.7 Combine like terms: 32.7 + -32.7 = 0.0 0.0 + -14x + x2 = 0 + -32.7 -14x + x2 = 0 + -32.7 Combine like terms: 0 + -32.7 = -32.7 -14x + x2 = -32.7 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = -32.7 + 49 Reorder the terms: 49 + -14x + x2 = -32.7 + 49 Combine like terms: -32.7 + 49 = 16.3 49 + -14x + x2 = 16.3 Factor a perfect square on the left side: (x + -7)(x + -7) = 16.3 Calculate the square root of the right side: 4.037325848 Break this problem into two subproblems by setting (x + -7) equal to 4.037325848 and -4.037325848.Subproblem 1
x + -7 = 4.037325848 Simplifying x + -7 = 4.037325848 Reorder the terms: -7 + x = 4.037325848 Solving -7 + x = 4.037325848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 4.037325848 + 7 Combine like terms: -7 + 7 = 0 0 + x = 4.037325848 + 7 x = 4.037325848 + 7 Combine like terms: 4.037325848 + 7 = 11.037325848 x = 11.037325848 Simplifying x = 11.037325848Subproblem 2
x + -7 = -4.037325848 Simplifying x + -7 = -4.037325848 Reorder the terms: -7 + x = -4.037325848 Solving -7 + x = -4.037325848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -4.037325848 + 7 Combine like terms: -7 + 7 = 0 0 + x = -4.037325848 + 7 x = -4.037325848 + 7 Combine like terms: -4.037325848 + 7 = 2.962674152 x = 2.962674152 Simplifying x = 2.962674152Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.037325848, 2.962674152}
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