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Simplifying -2.1x2 + 988x + 13723 = 0 Reorder the terms: 13723 + 988x + -2.1x2 = 0 Solving 13723 + 988x + -2.1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -2.1 the coefficient of the squared term: Divide each side by '-2.1'. -6534.761905 + -470.4761905x + x2 = 0 Move the constant term to the right: Add '6534.761905' to each side of the equation. -6534.761905 + -470.4761905x + 6534.761905 + x2 = 0 + 6534.761905 Reorder the terms: -6534.761905 + 6534.761905 + -470.4761905x + x2 = 0 + 6534.761905 Combine like terms: -6534.761905 + 6534.761905 = 0.000000 0.000000 + -470.4761905x + x2 = 0 + 6534.761905 -470.4761905x + x2 = 0 + 6534.761905 Combine like terms: 0 + 6534.761905 = 6534.761905 -470.4761905x + x2 = 6534.761905 The x term is -470.4761905x. Take half its coefficient (-235.2380953). Square it (55336.96148) and add it to both sides. Add '55336.96148' to each side of the equation. -470.4761905x + 55336.96148 + x2 = 6534.761905 + 55336.96148 Reorder the terms: 55336.96148 + -470.4761905x + x2 = 6534.761905 + 55336.96148 Combine like terms: 6534.761905 + 55336.96148 = 61871.723385 55336.96148 + -470.4761905x + x2 = 61871.723385 Factor a perfect square on the left side: (x + -235.2380953)(x + -235.2380953) = 61871.723385 Calculate the square root of the right side: 248.740272945 Break this problem into two subproblems by setting (x + -235.2380953) equal to 248.740272945 and -248.740272945.Subproblem 1
x + -235.2380953 = 248.740272945 Simplifying x + -235.2380953 = 248.740272945 Reorder the terms: -235.2380953 + x = 248.740272945 Solving -235.2380953 + x = 248.740272945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '235.2380953' to each side of the equation. -235.2380953 + 235.2380953 + x = 248.740272945 + 235.2380953 Combine like terms: -235.2380953 + 235.2380953 = 0.0000000 0.0000000 + x = 248.740272945 + 235.2380953 x = 248.740272945 + 235.2380953 Combine like terms: 248.740272945 + 235.2380953 = 483.978368245 x = 483.978368245 Simplifying x = 483.978368245Subproblem 2
x + -235.2380953 = -248.740272945 Simplifying x + -235.2380953 = -248.740272945 Reorder the terms: -235.2380953 + x = -248.740272945 Solving -235.2380953 + x = -248.740272945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '235.2380953' to each side of the equation. -235.2380953 + 235.2380953 + x = -248.740272945 + 235.2380953 Combine like terms: -235.2380953 + 235.2380953 = 0.0000000 0.0000000 + x = -248.740272945 + 235.2380953 x = -248.740272945 + 235.2380953 Combine like terms: -248.740272945 + 235.2380953 = -13.502177645 x = -13.502177645 Simplifying x = -13.502177645Solution
The solution to the problem is based on the solutions from the subproblems. x = {483.978368245, -13.502177645}
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