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Simplifying -30x2 + 700x + 2100 = 0 Reorder the terms: 2100 + 700x + -30x2 = 0 Solving 2100 + 700x + -30x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(210 + 70x + -3x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(210 + 70x + -3x2)' equal to zero and attempt to solve: Simplifying 210 + 70x + -3x2 = 0 Solving 210 + 70x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -70 + -23.33333333x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + -23.33333333x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + -23.33333333x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + -23.33333333x + x2 = 0 + 70 -23.33333333x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 -23.33333333x + x2 = 70 The x term is -23.33333333x. Take half its coefficient (-11.66666667). Square it (136.1111112) and add it to both sides. Add '136.1111112' to each side of the equation. -23.33333333x + 136.1111112 + x2 = 70 + 136.1111112 Reorder the terms: 136.1111112 + -23.33333333x + x2 = 70 + 136.1111112 Combine like terms: 70 + 136.1111112 = 206.1111112 136.1111112 + -23.33333333x + x2 = 206.1111112 Factor a perfect square on the left side: (x + -11.66666667)(x + -11.66666667) = 206.1111112 Calculate the square root of the right side: 14.356570315 Break this problem into two subproblems by setting (x + -11.66666667) equal to 14.356570315 and -14.356570315.Subproblem 1
x + -11.66666667 = 14.356570315 Simplifying x + -11.66666667 = 14.356570315 Reorder the terms: -11.66666667 + x = 14.356570315 Solving -11.66666667 + x = 14.356570315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.66666667' to each side of the equation. -11.66666667 + 11.66666667 + x = 14.356570315 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + x = 14.356570315 + 11.66666667 x = 14.356570315 + 11.66666667 Combine like terms: 14.356570315 + 11.66666667 = 26.023236985 x = 26.023236985 Simplifying x = 26.023236985Subproblem 2
x + -11.66666667 = -14.356570315 Simplifying x + -11.66666667 = -14.356570315 Reorder the terms: -11.66666667 + x = -14.356570315 Solving -11.66666667 + x = -14.356570315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.66666667' to each side of the equation. -11.66666667 + 11.66666667 + x = -14.356570315 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + x = -14.356570315 + 11.66666667 x = -14.356570315 + 11.66666667 Combine like terms: -14.356570315 + 11.66666667 = -2.689903645 x = -2.689903645 Simplifying x = -2.689903645Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.023236985, -2.689903645}Solution
x = {26.023236985, -2.689903645}
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