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Simplifying -30 + 14x + 3x2 = 0 Solving -30 + 14x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10 + 4.666666667x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 4.666666667x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 4.666666667x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 4.666666667x + x2 = 0 + 10 4.666666667x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 4.666666667x + x2 = 10 The x term is 4.666666667x. Take half its coefficient (2.333333334). Square it (5.444444448) and add it to both sides. Add '5.444444448' to each side of the equation. 4.666666667x + 5.444444448 + x2 = 10 + 5.444444448 Reorder the terms: 5.444444448 + 4.666666667x + x2 = 10 + 5.444444448 Combine like terms: 10 + 5.444444448 = 15.444444448 5.444444448 + 4.666666667x + x2 = 15.444444448 Factor a perfect square on the left side: (x + 2.333333334)(x + 2.333333334) = 15.444444448 Calculate the square root of the right side: 3.929942041 Break this problem into two subproblems by setting (x + 2.333333334) equal to 3.929942041 and -3.929942041.Subproblem 1
x + 2.333333334 = 3.929942041 Simplifying x + 2.333333334 = 3.929942041 Reorder the terms: 2.333333334 + x = 3.929942041 Solving 2.333333334 + x = 3.929942041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 3.929942041 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 3.929942041 + -2.333333334 x = 3.929942041 + -2.333333334 Combine like terms: 3.929942041 + -2.333333334 = 1.596608707 x = 1.596608707 Simplifying x = 1.596608707Subproblem 2
x + 2.333333334 = -3.929942041 Simplifying x + 2.333333334 = -3.929942041 Reorder the terms: 2.333333334 + x = -3.929942041 Solving 2.333333334 + x = -3.929942041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -3.929942041 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -3.929942041 + -2.333333334 x = -3.929942041 + -2.333333334 Combine like terms: -3.929942041 + -2.333333334 = -6.263275375 x = -6.263275375 Simplifying x = -6.263275375Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.596608707, -6.263275375}
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