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Simplifying 15x2 + 9x + -700 = 0 Reorder the terms: -700 + 9x + 15x2 = 0 Solving -700 + 9x + 15x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -46.66666667 + 0.6x + x2 = 0 Move the constant term to the right: Add '46.66666667' to each side of the equation. -46.66666667 + 0.6x + 46.66666667 + x2 = 0 + 46.66666667 Reorder the terms: -46.66666667 + 46.66666667 + 0.6x + x2 = 0 + 46.66666667 Combine like terms: -46.66666667 + 46.66666667 = 0.00000000 0.00000000 + 0.6x + x2 = 0 + 46.66666667 0.6x + x2 = 0 + 46.66666667 Combine like terms: 0 + 46.66666667 = 46.66666667 0.6x + x2 = 46.66666667 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 46.66666667 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 46.66666667 + 0.09 Combine like terms: 46.66666667 + 0.09 = 46.75666667 0.09 + 0.6x + x2 = 46.75666667 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 46.75666667 Calculate the square root of the right side: 6.837884663 Break this problem into two subproblems by setting (x + 0.3) equal to 6.837884663 and -6.837884663.Subproblem 1
x + 0.3 = 6.837884663 Simplifying x + 0.3 = 6.837884663 Reorder the terms: 0.3 + x = 6.837884663 Solving 0.3 + x = 6.837884663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 6.837884663 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 6.837884663 + -0.3 x = 6.837884663 + -0.3 Combine like terms: 6.837884663 + -0.3 = 6.537884663 x = 6.537884663 Simplifying x = 6.537884663Subproblem 2
x + 0.3 = -6.837884663 Simplifying x + 0.3 = -6.837884663 Reorder the terms: 0.3 + x = -6.837884663 Solving 0.3 + x = -6.837884663 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -6.837884663 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -6.837884663 + -0.3 x = -6.837884663 + -0.3 Combine like terms: -6.837884663 + -0.3 = -7.137884663 x = -7.137884663 Simplifying x = -7.137884663Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.537884663, -7.137884663}
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